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# Exponential equation formula

### Algebra - Solving Exponential Equation

1. There are two methods for solving exponential equations. One method is fairly simple but requires a very special form of the exponential equation. The other will work on more complicated exponential equations but can be a little messy at times. Let's start off by looking at the simpler method
2. Equations of Exponential Functions | College Algebra. Education Details: Solve the resulting system of two equations to find a a and b b.Using the a and b found in the steps above, write the exponential function in the form f (x) = abx f (x) = a b x. Example: Writing an Exponential Model When the Initial Value Is Known In 2006, 80 deer were introduced into a wildlife refuge
3. How To: Given an exponential equation Of the form bS =bT b S = b T, where S and T are algebraic expressions with an unknown, solve for the unknown Use the rules of exponents to simplify, if necessary, so that the resulting equation has the form bS = bT b S = b T. Use the one-to-one property to set the exponents equal to each other

Exponential equations are equations in which variables occur as exponents. For example, exponential equations are in the form a x = b y. To solve exponential equations with same base, use the property of equality of exponential functions. If b is a positive number other than 1, then b x = b y if and only if x = y Exponential equations have the unknown variable in the exponent. Here are some examples: 3x + 1 = 9 5t + 3 × 5t − 1 = 400 If we can write a single term with the same base on each side of the equation, we can equate the exponents Exponential Distribution Formula The exponential function is a special type where the input variable works as the exponent. A function f (x) = bx + c or function f (x) = a, both are the exponential functions. It is used everywhere, if we talk about the C programming language then the exponential function is defined as the e raised to the power x

Write the general f orm of an exponential equation. Substitute the initial value 3 f or a. Substitute in 12 f or y and 2 f or x. Divide by 3 2 x = 4 8 2 x = 16 16 x + 1 = 256 (1 2) x + 1 = 512 As you might've noticed, an exponential equation is just a special type of equation. It's an equation that has exponents that are v a r i a b l e s Exponential Function Reference. This is the general Exponential Function (see below for e x): f(x) = a x. a is any value greater than 0. Properties depend on value of a When a=1, the graph is a horizontal line at y=1; Apart from that there are two cases to look at: a between 0 and 1 ### Exponential Function Formula Equatio

• Free exponential equation calculator - solve exponential equations step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy
• Solving Exponential Equations . An exponential equation 15 is an equation that includes a variable as one of its exponents. In this section we describe two methods for solving exponential equations. First, recall that exponential functions defined by $$f (x) = b^{x}$$ where $$b > 0$$ and $$b ≠ 1$$, are one-to-one; each value in the range corresponds to exactly one element in the domain
• To solve exponential equations with the same base, which is the big number in an exponential expression, start by rewriting the equation without the bases so you're left with just the exponents. Then, solve the new equation by isolating the variable on one side

### Exponential Equations College Algebr

One very important exponential equation is the compound-interest formula:...where A is the ending amount, P is the beginning amount (or principal), r is the interest rate (expressed as a decimal), n is the number of compoundings a year, and t is the total number of years.Regarding the variables, n refers to the number of compoundings in any one year, not to the total number of. The four variables used for its computation are the principal amount, time, interest rate and the number of the compounding period. read more, the equation is used to calculate the final value by multiplying the initial value and the exponential function, which is raised to the power of the annual growth rate into the number of years

### Solving Exponential Equations - Varsity Tutor

It decreases about 12% for every 1000 m: an exponential decay. The pressure at sea level is about 1013 hPa (depending on weather). Write the formula (with its k value), Find the pressure on the roof of the Empire State Building (381 m), and at the top of Mount Everest (8848 m) Start with the formula: y(t) = a × e kt. We kno Sec 5.7 - Exponential & Logarithmic Functions (Solving Exponential Equations) Name: 1. Solve the following basic exponential equations by rewriting each side using the same base. a. ë 3 ? 5= 81 7 b.2 6 ë ? 7= 128 c. 2 5= 4 2. Solve the following basic exponential equation by rewriting each as logarithmic equation and approximating the value of x How to: Given an exponential equation with the form bS = bT, where S and T are algebraic expressions with an unknown, solve for the unknown. Use the rules of exponents to simplify, if necessary, so that the resulting equation has the form bS = bT. Use the one-to-one property to set the exponents equal Now we can use the logarithm property that says, log 10 f ( x) = f ( x) log ⁡ 10 f ( x) = f ( x) to simplify the right side of the equation. Doing this gives, log 9 = 4 + 6 x log ⁡ 9 = 4 + 6 x Show Step 3. Finally, all we need to do is solve for x x. Recall that the equations at this step tend to look messier than we are used to dealing with In mathematics, the exponential function is the function where e = 2.71828... is Euler's constant. More generally, an exponential function is a function of the form where b is a positive real number, and the argument x occurs as an exponent

### Exponential equations Exponents Siyavul

• For linear equations, we have y = m (slope) x + b (y intercept) and for exponential equations we have y = a (initial value)*r (ratio or base)^x. So in each case, we need to find two things. In both cases, the y intercept and initial value are found where x = 0 (y intercept) and the table gives us these, so linear b = 5 and exponential a = 3
• let's get some practice solving some exponential equations and we have one right over here we have 26 to the 9x plus 5 power equals 1 so pause the video and see if you can tell me what X is going to be well the key here is to realize the 26 to the 0th power to the zeroth power is equal to 1 anything to the zeroth power is going to be equal to 1 0 to 0 power we can discuss it some other time.
• This video explains how to use the change of base formula for logarithms to solve basic exponential equations.Library: http://mathispower4u.comSearch: http..

### Exponential Formula Function, Distribution, Growth

• To compute the value of y, we will use the EXP function in excel so the exponential formula will be = a* EXP (-2*x) Applying the exponential formula with the relative reference, we have =$B$5*EXP (-2*B
• The equation is: y = − 32 × ( 1 2) x y=-32 \times \left (\dfrac {1} {2} \right)^x y = − 32 × ( 2 1 ) x. Result. 3 of 3. a-. y = 3 × 6 x y=3 \times 6^x y = 3 × 6 x. b-. y = − 32 × ( 1 2) x y=-32 \times \left (\dfrac {1} {2} \right)^x y = − 32 × ( 2 1 ) x. Reveal next step
• g transformations on exponential functions, the domain, range, y-intercept, and asymptote will change
• Then I right clicked on the data line to have Excel create a Trendline using Exponential. I then clicked the option to show the equation for the trendline. Here is the equation: y = 1939.2e-.082x I'd like to enter a formula in Excel, so that for a known X value, I can get the corresponding Y value on the trendline. Thanks

An exponential equation is one in which a variable occurs in the exponent, for example, . When both sides of the equation have the same base, the exponents on either side are equal by the property if , then . Important logarithmic rules used to solve exponential equations include: Exponential equations are also solved using logs, either common. Exponential Function Formula. The exponential function is an important mathematical function, the exponential function formula can be written in the form of: Function f (x) = ax. Where the value of a > 0 and the value of a is not equal to 1. X can be any real number. If the value of the variable is negative, the function is undefined for (range. Euler's formula is ubiquitous in mathematics, physics, and engineering. The physicist Richard Feynman called the equation our jewel and the most remarkable formula in mathematics. When x = π, Euler's formula evaluates to eiπ + 1 = 0, which is known as Euler's identity ### Find the equation of an exponential function College Algebr

Build your Career in Data Science, Web Development, Marketing & More.. Flexible, Online Learning at Your Own Pace. Invest 2-3 Hours A Week & Advance Your Caree equation in which year is in the exponent. Go to page 1.6 to explore an equation of the form compound m n year. You will need to plot the function f(x) m n x. This is called an exponential equation. To adjust n, you may need to zoom in on values near 1. Q9 What values of m and n give the best ﬁ t for the data? Do you think compoun Similarly, x 3 = 27 is an exponential equation while x + 2 = 29 is not an exponential equation. Exponents signify repeated self-multiplication. E.g.,: 2 3 = 2*2*2. Exponents are a shorthand way of representing repeated multiplication. Consider the following examples, which are all exponential equations because a term is multiplied by itself.

To solve exponential equations, we need to consider the rule of exponents. These rules help us a lot in solving these type of equations. In solving exponential equations, the following theorem is often useful: Here is how to solve exponential equations: Manage the equation using the rule of exponents and some handy theorems in algebra. Use the theorem above that we just proved A. Increasing exponential B. Decreasing exponential C. Increasing linear D. Decreasing linear E. Increasing cubic 2. Each year the value of an investment increases by 3.5% of the previous year's value. The initial value of the investment was \$400. Which equation gives the value of the investment , in dollars, years after the initia Exponential Function • A function in the form y = ax - Where a > 0 and a ≠ 1 - Another form is: y = abx + c • In this case, a is the coefficient • To graph exponential function, make a table • Initial Value - - The value of the function when x = 0 - Also the y-intercep Exponential Equations - examples of problems with solutions for secondary schools and universitie Exponential growth is modeled an exponential equation. The population of a species that grows exponentially over time can be modeled by. P ( t) = P 0 e k t P (t)=P_0e^ {kt} P ( t) = P 0 e k t . where P ( t) P (t) P ( t) is the population after time t t t, P 0 P_0 P 0 is the original population when t = 0 t=0 t = 0, and k k k is the growth constant

Following is an exponential decay function: y = a (1-b) x. where: y is the final amount remaining after the decay over a period of time. a is the original amount. x represents time. The decay factor is (1-b). The variable, b, is the percent change in decimal form. Because this is an exponential decay factor, this article focuses on. An exponential equation is an equation in which the unknown occurs as part of the exponent or index. For example, 2x = 16 2 x = 16 and 25 ×3x = 9 25 × 3 x = 9 are both exponential equations. There are a number of methods we can use to solve exponential equations. These include graphing, using technology, and by using logarithms Exponential Growth = 100 * (1 + 10%) ^36; Exponential Growth = 3,091.27 Exponential Growth is 3,091.27. Explanation. The formula is used where there is continuous growth in a particular variable such population growth, bacteria growth, if the quantity or can variable grows by a fixed percentage then the exponential formula can come in handy to be used in statistic Exponential Equations: Continuous Compound Interest Application One of the most common applications of the exponential functions is the calculation of compound and continuously compounded interest. This discussion will focus on the continuously compounded interest application Exponential equations have a variable as an exponent and take the form y= abx. The y-values of (or solutions to) an exponential equation follow a geometric progression and are the result of repeated multiplication by the same amount. The shape of graphs of exponential equations indicate exponential growth or decay

### Solve Exponential Equations: How to solve exponential

Exponential Equations . Given 9 a = 2 7 10 9^a = 27^{10} 9 a = 2 7 1 0, where a a a is a positive integer, what is the value of a a a? Submit Show explanation View wiki. by Brilliant Staff. How many real values of x x x satisfy the following equation 9 x − 6 ⋅ 3 x − 55 = 0 9^x - 6 \cdot. Step-by-Step Examples. Algebra. Logarithmic Expressions and Equations. Write in Exponential Form. 2 = ln (3x) 2 = ln ( 3 x) For logarithmic equations, logb(x) = y log b ( x) = y is equivalent to by = x b y = x such that x > 0 x > 0, b > 0 b > 0, and b ≠ 1 b ≠ 1 Finding the Equation of an Exponential Function From Its Graph. Step 1: Determine the horizontal asymptote of the graph.This determines the vertical translation from the simplest exponential. An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.For example, 3 x = 81, 5 x - 3 = 625, 6 2y - 7 = 121, etc are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay, etc So, here's the formula for population growth (which also applies to people). I'm just going to change the letters a little: The is pronounced P not. The little o is a zero for time = 0... when you start. * time is usually in hours or years Let's just do one -- they're really easy! In 1950, the world's population was 2,555,982,611

### Exponential Function Referenc

One way is if we are given an exponential function. The second way involves coming up with an exponential equation based on information given. Let's look at each of these separately. Let's Practice: The population of a city is P = 250,342e 0.012t where t = 0 represents the population in the year 2000 Exponential and Logarithmic Equations. Many of the same principles of equation solving extend to equations that contain either: 1) exponential expressions where the variable appears in the exponent, or 2) logarithmic expressions. x) are inverses of one another. Each can be used to eliminate the other as the next two examples show The two types of exponential functions are exponential growth and exponential decay. Four variables (percent change, time, the amount at the beginning of the time period, and the amount at the end of the time period) play roles in exponential functions. Use an exponential decay function to find the amount at the beginning of the time period

The way exponential equations have appeared in the news is in our current times we are in a pandemic. The coronavirus pandemic to be specific. When the pandemic first started and quarantine had been placed, the news was talking about the number of cases that were being reported Introduction. In addition to linear, quadratic, rational, and radical functions, there are exponential functions. Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent. An example of an exponential function is the growth of bacteria A function f(x) = a(b)cx can be represented as f(x) = a(bc)x. When creating exponential functions from real-world scenarios, use the following steps:First, choose the appropriate formula to model the problem.Second, identify all important mathematical information in the problem.Last, substitute the information into the formula and simplify Purplemath. Most exponential equations do not solve neatly; there will be no way to convert the bases to being the same, such as the conversion of 4 and 8 into powers of 2. In solving these more-complicated equations, you will have to use logarithms. Taking logarithms will allow us to take advantage of the log rule that says that powers inside. Example 1. Solve for x. This is an exponential equation because the x is in the exponent. In order to solve for x, we need to get rid of the 5. The 5 is the base of the exponential expression. To cancel it, we need to use a logarithm with the same base. Step 1: Take the log of both sides

### Exponential Equation Calculator - Symbola

Solve Exponential Equations Using Logarithms. In the section on exponential functions, we solved some equations by writing both sides of the equation with the same base. Next we wrote a new equation by setting the exponents equal. It is not always possible or convenient to write the expressions with the same base An exponential equation is an equation where x (the variable) is in the exponent (index). If you graph an exponential function (this I will explain in another section) you will get a graph looking similar to the one on the picture next to this text. When you look at the first video I will explain to you step by step how to solve exponential. exponential equations can be written in logarithmic form. To change from exponential form to logarithmic form, identify the base of the exponential equation and move the base to the other side of the equal sign and add the word log The exponential equation is the equation where each side can be represented with the same base and it can be solved with the help of property. It can also be used to design a graph for compound interest, radioactive decay, and growth of population etc. In mathematics, the exponential equation formula can be given as - Solving Exponential Equations without Logarithms. An exponential equation involves an unknown variable in the exponent. In this lesson, we will focus on the exponential equations that do not require the use of logarithm. In algebra, this topic is also known as solving exponential equations with the same base

### 9.5: Solving Exponential and Logarithmic Equations ..

I have a problem creating an exponential function in equation mode in Latex. I would like to have this exponential function: exponential^((y^2)/4). Does anyone know have to do that? Davi Free equations calculator - solve linear, quadratic, polynomial, radical, exponential and logarithmic equations with all the steps. Type in any equation to get the solution, steps and graph This website uses cookies to ensure you get the best experience Free Practice for SAT, ACT and Compass Math tests. Solve Exponential Equations. Solve the equation: Solution Note that 27, 9 and 3 may be written as powers of 3 as follows: 27 = 3 3, 9 = 3 2 and 3 = 3 1 Using the above and also the formula $$\dfrac{1}{x^n} = x^{-n}$$, we rewrite the given equation as follows: (3 3) 2x (3-2) x - 2 = (3 2)-x (3-1) 2 - x We now use the formula (x m) n = x m n. What are exponential equations? Exponential equations are those where x is in the exponent of the power. To understand all the steps in solving this type of equation, it is necessary that you perfectly master the properties of the powers. Let's start! Solved exercises of exponential equations Exponential Equation We therefore propose a new class of time integration methods for large systems of nonlinear differential equations which use Krylov approximations to the exponential function of the Jacobian.

### How to Solve Exponential Equations - wikiHo

This is a integrated presentation of the theory of exponential diophantine equations. The authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms in logarithms of algebraic numbers. Topics covered include the Thue equations. The following steps can be followed to solve the exponential equations using logarithms: Step 1: Any exponential expression should be kept at one side of the equation. Step 2: It needs to get a log on both sides of the equation. Any bases can be used for log Solving Exponential Equations Using Logarithms. Sometimes the terms of an exponential equation cannot be rewritten with a common base. In these cases, we solve by taking the logarithm of each side. Recall, since log (a) = log (b) log (a) = log (b) is equivalent to a = b, a = b, we may apply logarithms with the same base on both sides of an. The authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms in logarithms of algebraic numbers. Topics covered include the Thue equations, the generalised hyperelliptic equation, and the Fermat and Catalan equations

Exponential growth is a specific way in which an amount of some quantity can increase over time. It occurs when the instantaneous exchange rate of an amount with respect to time is proportional to the amount itself Solving Exponential Equations Solve the Exponential Equation 12.9(1.038) = 170 by following the steps below. Note: You must give each answer written as an equation. 12.9(1.038) = 170 Original Problem Statement ISOLATE the exponential part of the equation Change the equation to LOGARITHMIC form ISOLATE the variable Determine your Final Results in Exact Form Use the Exact Form to find the final. Write exponential equations using data from tables. You'll gain access to interventions, extensions, task implementation guides, and more for this instructional video. In this lesson you will learn how to write an exponential equation by finding a pattern in a table Transcribed image text: Solving Exponential Equations Solve the Exponential Equation 13.9(1.063) = 130 by following the steps below. Note: You must give each answer written as an equation. 13.9(1.063) = 130 Original Problem Statement ISOLATE the exponential part of the equation Preview Change the equation to LOGARITHMIC form ISOLATE the variable Determine your Final Results in Exact Form. Exponential Equations. An exponential equation is an equation in which the pronumeral appears as an index. For example, 2 3 x = 64 is an exponential equation. We can see from the graph that the curve y = 2 3 x and y = 64 the line only meet once, so there is one unique solution to the exponential equation. We can solve the equation as follows: 2. Solving Exponential Equations Deciding How to Solve Exponential Equations When asked to solve an exponential equation such as 2 x +6 = 32 or 5 2x-3 = 18, the first thing we need to do is to decide which way is the best way to solve the problem

The Natural Exponential Function: The natural exponential function is the exponential function . f xe= x with base e. It is often referred to as the exponential function. Since 2 < e < 3, the graph of the natural exponential function lies between the graphs of y = 2x and y = 3x, as shown below. By: Crystal Hul An exponential function f with base b is defined by f ( or x) = bx y = bx, where b > 0, b ≠ 1, and x is any real number. Note: Any transformation of y = bx is also an exponential function. Example 1: Determine which functions are exponential functions. For those that are not, explain why they are not exponential functions

To solve an exponential equation, take the log of both sides, and solve for the variable. Example 1: Solve for x in the equation . Solution: Step 1: Take the natural log of both sides: Step 2: Simplify the left side of the above equation using Logarithmic Rule 3: Step 3: Simplify the left side of the above equation: Since Ln(e)=1, the equation reads Ln(80) is the exact answer and x=4. Exponential smoothing is primarily used for time-series data analysis. Exponential Smoothing Formula. The exponential smoothing formula is derived by: st = θxt+(1 - θ)st-1= st-1+ θ(xt - st-1) Here, st is a former smoothed statistic, it is the simple weighted average of present observation xt. st-1 is former smoothed statisti Exponential Equations Worksheet #1 Name_____ Solve the Exponential Equation. Author: Brooklyn Eve Punziano Created Date: 3/4/2013 11:17:35 A exponential equations. As a general principle, whenever we seek the value of a variable in an equation: If the variable appears as an exponent, we should think about using logarithms. Smith (SHSU) Elementary Functions 2013 2 / 16 Solving exponential and logarithmic equations Here is a set of sample problems Two other ways to motivate an extension of the exponential function to complex numbers, and to show that Euler's formula will be satis ed for such an extension are given in the next two sections. 3.1 ei as a solution of a di erential equation The exponential functions f(x) = exp(cx) for ca real number has the property d dx f= c

Writing Exponential Equations from Points and Graphs. You may be asked to write exponential equations, such as the following: Write an equation to describe the exponential function in form $$y=a{{b}^{x}}$$, with a given base and a given point. Write an exponential function in form $$y=a{{b}^{x}}$$ whose graph passes through two given points Solving Exponential Equations 1 - Cool Math has free online cool math lessons, cool math games and fun math activities. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too

Solving advanced exponential equations Problem 1 Solve an equation + = + . Solution + = + = = = = 3 Take logarithm base 3 of both sides = = 1 x = . ANSWER Problem 2 Solve an equation + = . Solution The given exponential equation + = (1) is equivalent to + = , or + = . (2) Introduce new variables u = 2^x, v = 3^x The following problems involve the integration of exponential functions. We will assume knowledge of the following well-known differentiation formulas : , where , and. , where a is any positive constant not equal to 1 and is the natural (base e) logarithm of a . These formulas lead immediately to the following indefinite integrals

You might be also interested in: - Exponential Function. - Linear Equations and Inequalities. - Systems of Equations and Inequalities. - Quadratic Equations and Inequalities. - Irrational Equations and Inequalities. - Logarithmic Equations and Inequalities. - Trigonometric Equations and Inequalities. - Combinatorial Equations and Inequalities Exponential Equations Solver. Two online calculators and solvers for exponential equations of the form $$b^x = a$$ are presented. We consider two cases: 1) Equations of the form $e^x = a$ with base $$b = e$$ whose solution is given by $x = \ln a \quad \text{for} \; a \gt 0$ $\text{No real solutions for} \; a \le 0$ 2) Equations of the form $b^x = a$ with any base \( b \gt 0. Note: To solve an exponential equation, isolate the exponential term, take the logarithm of both sides and solve. If you would like an in-depth review of exponents, the rules of exponents, exponential functions and exponential equations, click on exponential function under Algebra.. Solve for x in the following equation Simultaneous exponential equations are also known as a system of exponential equations. The word simultaneous implies that these equations are solved together. The values of unknown variables in one equation also satisfy the values for unknowns in the second equation. It means that the variables in one equation do not have a unique solution Exponential Regression. An exponential regression is the process of finding the equation of the exponential function that fits best for a set of data. As a result, we get an equation of the form y = a b x where a ≠ 0 . The relative predictive power of an exponential model is denoted by R 2 . The value of R 2 varies between 0 and 1

### Exponential Functions: Compound Interes

An exponential equation is an equation in which the variable appears in an exponent. A logarithmic equation is an equation that involves the logarithm of an expression containing a variable. To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number. If you cannot, take the common logarithm of both sides of the equation and then. The second-order exponential smoothing model is based on a linear trend and consists of two equations (see formula (11)). The first equation corresponds to that of first-order exponential smoothing except for the bracketed indices. In the second equation, the values calculated in the first equation are used as initial values and are smoothed. An exponential function can describe growth or decay. The function. g ( x) = ( 1 2) x. is an example of exponential decay. It gets rapidly smaller as x increases, as illustrated by its graph. In the exponential growth of f ( x), the function doubles every time you add one to its input x. In the exponential decay of g ( x), the function shrinks. Exponential & Logarithmic Functions; 1. Definitions: Exponential and Logarithmic Functions; 2. Graphs of Exponential and Logarithmic Equations; 3. Logarithm Laws; 4. Logarithms to Base 10; 5. Natural Logarithms (base e) Dow Jones Industrial Average; Calculating the value of e; 6. Exponential and Logarithmic Equations; World Population Live; 7   Exponentiation is a mathematical operation, written as b n, involving two numbers, the base b and the exponent or power n, and pronounced as b raised to the power of n . When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: = ⏟. The exponent is usually shown as a superscript to the right of the base Using Like Bases to Solve Exponential Equations. The first technique involves two functions with like bases. Recall that the one-to-one property of exponential functions tells us that, for any real numbers and where if and only if. In other words, when an exponential equation has the same base on each side, the exponents must be equal. This also applies when the exponents are algebraic. Exponential equation of the given data is (1/2)x. Example 2 : Determine whether each set of data displays exponential behavior. Solution : The domain values are at regular intervals of 10. The range values have a common difference 6. The data do not display exponential behavior, but rather linear behavior

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