Exponential Slope Calculator

An exponential function written as f(x) = 4^x is read as "four to the x power. Exponential Growth and Decay Calculator Use our online exponential growth and decay calculator by entering the initial value (x 0), decay rate (r) and time (t) in the below calculator and click calculate button to find the answer. Logarithmic vs Exponential | Exponential Function vs Logarithmic Function Functions are one of the most important classes of mathematical objects, which are extensively used in almost all subfields of mathematics. As you say the slope is r and the intercept is N. All calculators have simple and easy-to-use interface. The slope can be computed as the change in price divided by the change in quantity demanded between the two pairs. Here, for instance, the slope of y = 1 is zero. In case you need to calculate the cube root you can use our cube root calculator which is an excellent tool that will calculate the cube root of any number. Therefore, the Intercept value corresponds to Ln(c), and c in the exponential formula is equal to Exp(Intercept). " On the next blank page in their notebooks, I instructed students to write their name as large as possible. Some examples are population, compound interest and charge in a capacitor. The term "exp(x)" is the same as writing e x or e^x or "e to the x" or "e to the power of x". Welcome to Math Nspired About Math Nspired Middle Grades Math Ratios and Proportional Relationships The Number System Expressions and Equations Functions Geometry Statistics and Probability Algebra 1 Equivalence Equations Linear Functions Linear Inequalities Systems of Linear Equations Functions and Relations Quadratic Functions Exponential. More than 70 powerful online math calculators designed to help you solve all of your math problems. Right from ordered pair equation calculator to calculus, we have every part discussed. Finding an Exponential Model Use a graphing calculator to fi nd an exponential model for the data in Example 3. ln(x) calculator. In this article, I will explain how you can calculate slope values in Google Sheets with and without graphs. Exponential smoothing is a way to smooth out data for presentations or to make forecasts. The slope of a given curve at a specified point is the. An exponential function written as f(x) = 4^x is read as "four to the x power. com and read and learn about operations, mathematics and plenty additional math subject areas. Find an equation of the graph that passes through the point and has the given. The threshold levels were set to the natural logarithm of the 95% and 35% values used in figure 3. More Examples Here are more examples of how to graph equations in. skew 151 209210 slope of 177185 208 211212 915 of symmetry 47 645 tangent from MATH 101 at Mother of Divine Grace Homeschool. How to find the slope Learn how to compute the slope using the rise and the run or 2 points. Positive and negative slope. " Other examples of exponential functions include: $$ y=3^x $$ $$ f(x)=4. A least-squares regression fit of the data (using base 10 logarithms to transform columns (1) and (6)) indicates that the estimated slope for the Weibull distribution is 1. A line that slopes up from left to right has a positive gradient. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. Also see the resulting equation. Slope is a very important concept to understand in Algebra. Note: The above equation is only valid for the exponential equations. Remember, you will not use the Equation of a Line Maker on tests, but you can use it to check your work while you practice. The slope of a given curve at a specified point is the. Uncertainty in a single measurement Bob weighs himself on his bathroom scale. Now that we have the two ordered pairs, we can use them to calculate the slope of the demand function. When solving the slope, intercept, and correlation for a power or exponential calibration that has been transformed into a linear least square regression, the analyst can follow the equations as described for a linear least square regression. This is the general Exponential Function (see below for e x):. • The plot of x versus log 10(y) appears concave downward. The prediction interval focuses on the true y value for any set of x values. For example, the diagonal line shown to the right goes through points (–3, –4) and (1, 4) and has a slope of 2. Exponential. So, calculating the. Natural Logarithm Calculator. Did we mention that they're 100% free?. Then, the formula to find the equation of a line is y = mx + b. Each function accepts two arguments, both of which are are range of cells: the Y-block and the X-block cells. The exponential function is a power function having a base of e. The slope intercept form calculator will find the slope of the line passing through the two given points, its y-intercept and slope-intercept form of the line, with steps shown. A straight line has only one slope. What is Slope? Slope is a concept in geometry that describes the direction and steepness of a line on a Cartesian plane. Exponential regression is probably one of the simplest nonlinear regression models. 16 Evaluating logarithms 20 1. If you create many random samples that are normally distributed and for each sample you calculate a prediction interval for the y value corresponding to some set of x values, then about 95% of those intervals will contain the true y value. More Examples Here are more examples of how to graph equations in. At the first workshop of the summer, I got to participate in an activity that used M&Ms to model exponential decay. That is, b = D D == y x yy xx Rx Rx xx 21 21 21 21 - - ln ( ) - ln ( ) - (13. For values of 0, 1, and 2, the values of the function are 1, e or about 2. Use the following rules to enter expressions into the calculator. This test will be paper-based this year. Algebra Worksheets, Quizzes and Activities. independent variable. This is a good example of where a slope field can be slightly misleading. Math Plane ---->>>FLIGHT DELAYS!! Recently, Mathplane has been experiencing slow page loads. The Weibull parameter (beta) is the slope. Then we will move on to graphing slope and finally to using slope intercept form to create your graph. But if you're taking the idea literally, you don't need an exponential growth calculator; you can calculate rates of growth yourself, as long as you know some basic information concerning the population or object in question. Exponents are used in Computer Game Physics, pH and Richter Measuring Scales, Science, Engineering, Economics, Accounting, Finance, and many other disciplines. When you enter an expression into the calculator, the calculator will simplify the expression by expanding multiplication and combining like terms. More Examples Here are more examples of how to graph equations in. Change the a, b values in this exponential function to see the calculations of properties of exponential function. The only caveat was that they could only use straight lines. The square root of a number x is the same as x raised to the 0. In practice, this means substituting the points for y and x in the equation y = ab x. Slope alone cannot be used to participate in an ongoing trend, but it can be used with other indicators to identify potential entry points. The domain range calculator identifies any forbidden numbers and gives the answer in the correct notation. This is the Page of Learning about Electronics where you will find a wide range and assortment of calculators. Come to Algebra-equation. Exponential equations are also solved using logs, either common (log) or natural (ln). The slope of a given curve at a specified point is the. The calculator can also convert between half-life, mean lifetime, and decay constant given any one of the three values. This app calculates how much a distant object is obscured by the earth's curvature, and makes the following assumptions: the earth is a convex sphere of radius 6371 kilometres; light travels in straight lines; The source code and calculation method are available on GitHub. The exponential function also has analogues for which the argument is a matrix, or even an element of a Banach algebra or a Lie algebra. Learn vocabulary, terms, and more with flashcards, games, and other study tools. net and study mathematics i, notation and a great many additional algebra subjects. Since our data is in L1 and L2, that’s what we will enter into the calculator. Exponential growth is when numbers increase rapidly in an exponential fashion so for every x-value on a graph there is a larger y-value. exponential function, just as the slope of a line did with tables of points on a linear function. Linear Regression Formula. Assuming its growth is exponential, what is this population's doubling time? This island has a 14% growth rate over 20 years. Then, use the Equation of a Line Maker to check each of your answers. You can think of h as a dial that we can turn to get various. Gowher, The exponential regression model presupposes that this model is valid for your situation (based on theory or past experience). To calculate we should know the formulas. The slope intercept form calculator will find the slope of the line passing through the two given points, its y-intercept and slope-intercept form of the line, with steps shown. More about this Polynomial Regression Calculator so you can have a deeper perspective of the results that will be provided by this calculator. Slope at a Value Tangent Lines Exponential Growth and Decay. a is any value greater than 0. , a function in which the time value is the exponent. Note: The above equation is only valid for the exponential equations. In other words, the formula gives recent prices more weight than past prices. When = 1, the Weibull distribution models the exponential distribution. For the rest of the examples below, there are no built-in formulas. The first example is the exponential growth function y = 1 (3) x. Online math calculators and solvers. 18 Linear Function Exponential Function f(x) = mx + b f(x) = a ∙ bx b is the starting value, m is the rate or the slope. This type of function has many applications in population growth and economics. You are here: Home → Worksheets → Equation calculator Free equation calculator. WITH THE TI-NSPIRE CAS CALCULATOR An Essay Submitted to the Office of Graduate Studies College of Arts & Sciences of John Carroll University In Partial Fulfillment of the Requirements For the Degree of Master of Arts By Meghan A. The slope of an exponential function changes throughout the graph of the functionyou can get an EQUATION of the slope of the function by taking the first DERIVATIVE of the exponential function (dx/dy) if you know basic Differential equations/calculus. Hello, I am wondering if it is possible to calculate the slope in excel with a fixed y intercept? I know that if I construct a scatter plot I can insert a trend line which I can format to have a fixed y intercept and I can then display the equation on the graph. The term "exp(x)" is the same as writing e x or e^x or "e to the x" or "e to the power of x". Enter any Number into this free calculator. height for students in a. A straight line has only one slope. More Examples Here are more examples of how to graph equations in. Exponential Growth Calculator, Exponential Growth Problems. In a nutshell, regression analysis involves plotting pairs of independent and dependent variables in an XY chart and then finding a linear or exponential equation that describes the plotted data. Download free on iTunes. Graphs Exponential Functions Calculator. If you don't want to hire a math tutor, who is very expensive you can try this program Algebrator which I come upon and guarantee to be the best available. Let m be the slope and b be the y-intercept of a line. Mathematical and Scientific equations can be solved repeatedly without any difficulty with calculator. Learn how to calculate the exponential moving average in Excel and VBA, and get a free web-connected spreadsheet. Special indicators may display on the screen to provide additional information concerning functions or results. Euler’s Method on a Graphing Calculator by Jim Swift @ NAU Euler’s method is a way to nd approximate solutions to an Initial Value Problem (IVP). The calculator needs to know which two sets of data to use in order to find the trend line. Re: Calculation for logarithmic slope It's a least-squares regression of y onto LN(x). BMI Calculator » Triangle Calculators » Length and Distance Conversions » SD SE Mean Median Variance » Blood Type Child Parental Calculator » Unicode, UTF8, Hexidecimal » RGB, Hex, HTML Color Conversion » G-Force RPM Calculator » Chemical Molecular Weight Calculator » Mole, Moles to Grams Calculator » R Plot PCH Symbols » Dilution. Natural logarithm calculator. Thus, the exponential trendline equation gives you the slope of the transformed data automatically. Now click the checkbox to show the line tanget to `f(x)`. In Figure 4, the slew rate parameter (P2) is used to measure the slope of the math function. The slope eld applet written by Darryl Nester (linked to on our web site) uses Euler’s method or other more accurate methods to compute approximate solutions to an IVP. We will start here with defining and calculating slope by analyzing a graph. 5 cm in mature plant height. Comment/Request Good practice for students learning about computer output too, it's important to learn that not everything is hand-delivered in a nice equation; coefficients are often given in tables when technology does the work. We carry a lot of quality reference information on topics ranging from syllabus for elementary algebra to solving systems of linear equations. Slope Calculator Overview. Free Exponents & Radicals calculator - Apply exponent and radicals rules to multiply divide and simplify exponents and radicals step-by-step. com is the perfect site to stop by!. Once you get into advanced algebra and beyond, it can be difficult or time consuming to do mathematical calculations by hand. Calculate the slope of secants lines through the following points where 1) q1=30 and q2= 29. "Online Software Package" web sites [return to Table of Contents]. Objective 1: Students will be able to make an accurate sketch of vertically shifted and/or reflected exponential functions, and to identify the equation of a base two exponential function from its graph. Download free on iTunes. But, we are far from finished! We still need to calculate our ANOVA table, and calculate the resulting significance. As discussed in exponential theory the rate (q2) at time (t2) is related to the rate (q1) a time (t1) by: (1) In practice, especially when rates are being calculated by hand (or calculator) and knowing that exponential decline is a constant percentage decline, some people like to calculate the rate. Comment/Request Good practice for students learning about computer output too, it's important to learn that not everything is hand-delivered in a nice equation; coefficients are often given in tables when technology does the work. Enter each data point as a separate line. The online Exponential Decay Calculator is used to solve exponential decay problems. You would solve it via matrix inversion, which would be a PITA on a calculator -- at least on the last calculator I used before I stopped using them. Logarithmic vs Exponential | Exponential Function vs Logarithmic Function Functions are one of the most important classes of mathematical objects, which are extensively used in almost all subfields of mathematics. it is so much faster to get to the answer! Have a go at substituting the required values into the Gradient Formula, and working out the final answer. First go to the Algebra Calculator main page. In each portion, no-calculator and calculator, you’ll first. Calculate the power of large base integers and real numbers. Right from ordered pair equation calculator to calculus, we have every part discussed. This is an exponential growth curve, where the y-value increases and the slope of the curve increases as x increases. When you reflect across y=x, you take the reciprocal of the slope. So we can say "The cosine of 30° is 0. The relative predictive power of an exponential model is denoted by R 2. The mathematical constant e is the unique real number such that the derivative (the slope of the tangent line) of the function f(x) = e x is f '(x) = e x, and its value at the point x = 0, is exactly 1. Each x/y variable is represented on the graph as a dot or a. It is deliberately designed to be intuitive and very simple to use, and it is closely integrated with the SlopeCharts platform. The slope of the tangent line depends on being able to find the derivative of the function. When you enter an expression into the calculator, the calculator will simplify the expression by expanding multiplication and combining like terms. Exponential decay models of this form will increase very rapidly at first, and then level off to become asymptotic to the upper limit. And I also assume that you want to see more digits in those coefficients. Natural Logarithm Calculator. From the formula above we know that the cosine of an angle is the adjacent side divided by the hypotenuse. If you have two points, for example, (2, 6) and (3, 18), how do you find the equation if you know its exponential? I've heard about y=ab^x but I'm not sure what those variables represent. 98) and (6, 481. Since slope equals rise over run, the slope of the line is y 2 − y 1 over x 2 − x 1. Trigonometry Sine Equations Solver. The full calculation is always as follows:. We first isolate the exponential part by dividing both sides of the equation by 200. Free Calculus worksheets created with Infinite Calculus. ) Immediately use property 3 of logarithms to “bring down” the exponent. For y = brx the slope is rlog(b). BMI Calculator » Triangle Calculators » Length and Distance Conversions » SD SE Mean Median Variance » Blood Type Child Parental Calculator » Unicode, UTF8, Hexidecimal » RGB, Hex, HTML Color Conversion » G-Force RPM Calculator » Chemical Molecular Weight Calculator » Mole, Moles to Grams Calculator » R Plot PCH Symbols » Dilution. It's usually used for finance and economics. Exponential data forms a 'ramp' with increasing slope. Exponential values, returned as a scalar, vector, matrix, or multidimensional array. Exponential growth can be amazing! The idea is that something grows in relation to its current value, such as always doubling. The difference between the two decline rates is illustrated below. • The plot of x versus log 10(y) appears concave downward. Graphing calculators make is easy to work with exponents and functions. No matter how hard it is to get when you write any pattern and it does not still help you find the slope between two lines. For example, it can't tell you that the derivative of x 2 is 2x. How to Find Equations for Exponential Functions William Cherry Introduction. In this article, I will explain how you can calculate slope values in Google Sheets with and without graphs. x(t) is the value at time t. The exponent for exponential growth is always positive and greater than 1. If you have two points, for example, (2, 6) and (3, 18), how do you find the equation if you know its exponential? I've heard about y=ab^x but I'm not sure what those variables represent. a is any value greater than 0. Really, this just means we have a number greater than 1 getting raised to the x. Take a guided, problem-solving based approach to learning Calculus. The same properties of exponents apply for both positive and negative exponents. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. This is a general feature of inverse functions. All of them are capable of performing exact computations. Trace a graph online or use the Scientific Calculator to calculate any mathematical expression. • The plot of x versus log 10(y) appears concave downward. Exponential smoothing is a way to smooth out data for presentations or to make forecasts. f(x) = a x. In Figure 4, the slew rate parameter (P2) is used to measure the slope of the math function. Fitting Exponential Decay. 99 confidence intervals for the correlation coefficient (rho) that exists within the bivariate population from which the sample is drawn. The slope intercept form calculator will find the slope of the line passing through the two given points, its y-intercept and slope-intercept form of the line, with steps shown. 10(y) appears linear and the slope is n. They can, also, generate a step by step explanation at the click of a button. This widget can be use only for trinomials, if you need to factor polynomials, you can use our factoring polynomials calculator. Exponents are supported on variables using the ^ (caret) symbol. =10 is a horizontal line with a slope of zero, and so its. Note: The above equation is only valid for the exponential equations. Right from ordered pair equation calculator to calculus, we have every part discussed. 6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Over time this results in the exponential growth of your money. Available as a mobile and desktop website as well as native iOS and Android apps. Adjusted Slope 125/250d is equal to the average annualized exponential regression slope, over the past 125 and 250 trading days, multiplied by the coefficient of determination (R 2). The decimal will be moved to the right 9 places. This means the slope is undefined. 486 Chapter 8 Exponential and Logarithmic Functions Evaluate logarithmic functions. Definition of the slope. How to Find Equations for Exponential Functions William Cherry Introduction. Properties depend on value of "a". Active or Reactive? Many investors follow active strategies but end up being reactive, rotating in and out of stocks at the wrong time. Buying a poster from posters. Introduction to Exponential Functions. Mathematicians commonly use the letter m to represent slope. The exponent for exponential growth is always positive and greater than 1. it cost $40 to produce each canoe. Thus, the exponential trendline equation gives you the slope of the transformed data automatically. The online Exponential Decay Calculator is used to solve exponential decay problems. It is deliberately designed to be intuitive and very simple to use, and it is closely integrated with the SlopeCharts platform. Logarithmic functions can be graphed by hand without the use of a calculator if we use the fact that they are inverses of exponential functions. com and figure out factoring trinomials, mixed numbers and a great deal of other algebra subject areas. Slope at a Value Tangent Lines Exponential Growth and Decay. Of course, if we have a graphing calculator, the calculator can graph the function without the need for us to find points on the graph. Check your calculator for the rest of the examples, too. Equations like that in the next example occur frequently in applications. The slope of the linear section of the Ln trace is the reciprocal of the exponential time constant We can use the relative time cursors to read the slope of the Ln waveform. Two useful Excel functions are slope() and intercept(), which can be used to calculate the (you guessed it) the slope and intercept of a least-squares best-fit line through the data. You can access it at www. Spreadsheet users often need to calculate the slope of a line related to the data in their spreadsheet. 5 3) q1=30 and q2= 29. In each portion, no-calculator and calculator, you’ll first. How to select best Adjusted Slope 90d values Adjusted Slope 125/250d. Sorry for the delays. "Algebra" derives from the first word of the famous text composed by Al-Khwarizmi. As their names suggest both exponential function and logarithmic function are two special functions. com and understand linear systems, solving linear equations and a wide range of additional algebra subject areas. The graph of a linear function is a line with a constant slope. Type your algebra problem into the text box. Polynomial Regression is very similar to Simple Linear Regression, only that now one predictor and a certain number of its powers are used to predict a dependent. Find an equation of the graph that passes through the point and has the given. This defines the viewing window that will be used for the. They graph and complete problem sets for each, converting from one form of equation to another, and learning the benefits and uses of each. Sample Math Questions: Multiple-Choice. Trendlines, or best fit lines, help reveal linear relationships between variables. The slope of a given curve at a specified point is the. The gradient of a vertical line is undefined. " The simple way to think of the formula is: M=rise/run. It can handle horizontal and vertical tangent lines as well. On this page we explore this a bit more. Population growth, inflation, and radioactive decay are but a few examples of the various phenomenon that exponential functions can be used to. Start studying MATH 1 EOC REVIEW NC. A positive slope dictates a bullish bias, while a negative Slope dictates a bearish bias. Then use the slope formula to calculate the slope. Now we take the natural logarithm of both sides. Since slope equals rise over run, the slope of the line is y 2 − y 1 over x 2 − x 1. Weibull Distribution Calculator is an online probability and statistics tool for data analysis programmed to calculate precise accurate failure analysis and risk predictions with extremely small samples using a simple and useful graphical plot. Exponential. I somehow got confused with these equations. Find more Widget Gallery widgets in Wolfram|Alpha. This is because the y-axis of the exponential probability plotting paper represents the reliability, whereas the y-axis for most of the other life distributions represents the unreliability. Why you should learn it GOAL 2 GOAL 1 What you should learn 8. About "Slope Intercept Form Calculator" Slope Intercept Form Calculator : The calculator given in this section can be used to find the equation of a line when the slope and intercept of a line are given. 16 Evaluating logarithms 20 1. 116 FAQ-676 We are trying to use a single exponential decay equation to determine the half-life of a compound, but your equation is slightly different than the standard form. In the below two point slope form calculator, enter the X and Y coordinate values to find the straight line equation. The longer your investment stays in the account, the greater the ratio of interest to the original amount. where a and c are real numbers, and b is greater than 1. How to select best Adjusted Slope 90d values Adjusted Slope 125/250d. Some examples are population, compound interest and charge in a capacitor. They can, also, generate a step by step explanation at the click of a button. Then we will move on to graphing slope and finally to using slope intercept form to create your graph. Calculate the power of large base integers and real numbers. Exponential functions plot on semilog paper as straight lines. 1) After 5 hours, a bacteria culture with a growth rate of 30% per hour has grown to a population of 70,000. The decimal will be moved to the right 9 places. The first example is the exponential growth function y = 1 (3) x. If you know two points that fall on a particular exponential curve, you can define the curve by solving the general exponential function using those points. The purpose of this article is to describe the SLOPE function in Microsoft OfficeExcel 2003 and in later versions of Excel, to illustrate how the function is used, and to compare the results of the function in Excel 2003 and in later versions of Excel with the results of the SLOPE function in earlier versions of Excel. If you have two points, for example, (2, 6) and (3, 18), how do you find the equation if you know its exponential? I've heard about y=ab^x but I'm not sure what those variables represent. Did we mention that they're 100% free?. In this context, "e" is a universal constant, e = 2. slope of the trend line. Objective 1: Students will be able to make an accurate sketch of vertically shifted and/or reflected exponential functions, and to identify the equation of a base two exponential function from its graph. In this last expression, x 0 is (again) the point where we wish to find the slope and h is now an increment (either positive or negative) that defines how far away from x 0 we move to get another point to calculate the slope. Visualize the exponential function that passes through two points, which may be dragged within the x-y plane. t is the time in discrete intervals and selected time units. The domain of logarithmic function is positive real numbers and the range is all real numbers. The square root of a number x is the same as x raised to the 0. Show Instructions In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`. This calculator uses the following formula to derive the equation for the line of best fit. In general, the exponential decline is the most commonly used method. The gradient of a horizontal line is 0. How would you write return the Exponential Average of the Queued items in Quotes? I realize you will need to add an Alpha property to the class but I'm not sure how to complete the math for the calculation. When you study slope in Algebra, you are studying the incline along with other characteristics of a line. Exponential. Exponential relationships are relationships where one of the variables is an exponent. This interface is designed to allow the graphing and retrieving of the coefficients for polynomial regression. Discuss Slope. The results of a causal linear regression model were Y = 40 – 0. This is a general feature of inverse functions. Exponential Function Reference. Mathematicians commonly use the letter m to represent slope. Y-axis intercept. It also grew from a population of 20,000 to 22,800, but took 20 years to do it. For example, to express x 2, enter x^2. Now that we have the two ordered pairs, we can use them to calculate the slope of the demand function. Exponential. Factoring-polynomials. The Derivative Calculator has to detect these cases and insert the multiplication sign. Question 72913This question is from textbook mcgougal littell algebra 2: Write an exponential function of the form y=ab^x whose graph passes through the given points. Examples of exponential growth include contagious diseases for which a cure is unavailable, and biological populations whose growth is uninhibited by predation, environmental factors, and so on. To calculate the slope, we will consider an interval between and , compute the ratio of average rate of change of the exponential function over this interval and then see what happens as the interval becomes very small. Graphing Logarithmic Functions Using Their Inverses. The calculator can also convert between half-life, mean lifetime, and decay constant given any one of the three values. Exponential smoothing is a rule of thumb technique for smoothing time series data using the exponential window function. In the example the uncertainty in the slope is 0. It uses "well known" rules such as the linearity of the derivative, product rule, power rule, chain rule, so on. These types of logs can be expressed as: The natural logarithm of a number x (written as ln( x )) is the power to which e would have to be raised to equal x, where e is an irrational number approximately equal to 2. When bacteria are grown in a closed system (also called a batch culture), like a test tube, the population of cells almost always exhibits these growth dynamics: cells initially adjust to the new medium (lag phase) until they can start dividing regularly by the process of binary fission (exponential phase). Free graphing calculator instantly graphs your math problems. • The plot of x versus log 10(y) appears concave downward. An interesting thing to notice is that the slopes of the graphs of f and f -1 are multiplicative inverses of each other: The slope of the graph of f is 3 and the slope of the graph of f -1 is 1/3. Any lowercase letter may be used as a variable. Semi-log paper has one arithmetic and one logarithmic axis. Free slope calculator - find the slope of a line given two points, a function or the intercept step-by-step.