In Exercises 27-32, convert the given exponential function to the form indicated. Round all coefficients to four significant digits. [HINT: See “Before we go on” after Example 3.]
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Chapter 2 Solutions
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- Match the exponential function with one of the graphs labeled I,II,III and IV, shown below. (a) f(x)=2x (b) f(x)=2x (c) f(x)=2x (d) f(x)=2xarrow_forwardThe function f(x)=ex is called the___________ Exponential function. The number eis approximately equal to________.arrow_forwardFind the inverse function f1 for the exponential function f(x)=2ex+15.arrow_forward
- Recall that an exponential function is any equationwritten in the form f(x)=abx such that a and b arepositive numbers and b1. Any positive numberb; can be written as b=en for some value of n. Usethis fact to rewrite the formula for an exponentialfunction that uses the number e as a base.arrow_forwardLet f be The exponential function f(x)=ax , where a0 . (a) What is the function of f? (b) What is the range of f? (c) States graph of f for the following cases. (i) a0 (ii) 0a1arrow_forwardBy finding the appropriate logarithmic or exponential form of the equation, as in Example 1.arrow_forward
- Given a formula for an exponential function, is itpossible to determine whether the function grows ordecays exponentiallyjust by looking at the formula?Explain.arrow_forwardUse a graphing calculator to solve each problem. In Example 4, suppose that a birth control program changed the formula for poulation growth to Pt=1000e0.01t. How long will the food supply be adequate? EXAMPLE 4 Using a Graphing Calculator to Solve a popuiation Problem Suppose that a country with a population of 1000 people is growing exponentially according to the population function Pt=1000e0.02t Where t in years. Furthermore, assume that the food supply, measured in adequate food per day per person, is growing linearly according to the function fx=30.625x+2000 In how many years will the population outstrip the food supply?arrow_forwardLet f be the exponential function with base a. a Write an equation that defines f. b Write an equation for the exponential function f with base 3.arrow_forward
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