91Ó°ÊÓ

For the following exercises, find the formula for an exponential function that passes through the two points given. $$ \left(-1, \frac{3}{2}\right) \text { and }(3,24) $$

For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. Suppose an investment account is opened with an initial deposit of \(\$ 12,000\) earning 7.2\(\%\) interest compounded continuously. How much will the account be worth after 30 years?

For the following exercises, evaluate each function. Round answers to four decimal places, if necessary. $$ f(x)=1.2 e^{2 x}-0.3, \text { for } f(3) $$

In an exponential decay function, the base of the exponent is a value between 0 and \(1 .\) Thus, for some number \(b>1\) the exponential decay function can be written as \(f(x)=a \cdot\left(\frac{1}{b}\right)^{x}\) . Use this formula, along with the fact that \(b=e^{n},\) to show that an exponential decay function takes the form \(f(x)=a(e)^{-n x}\) for some positive number \(n\)

The fox population in a certain region has an annual growth rate of 9\(\%\) per year. In the year \(2012,\) there were \(23,900\) fox counted in the area. What is the fox population predicted to be in the year 2020\(?\)

A car was valued at \(\$ 38,000\) in the year \(2007 .\) By 2013 , the value had depreciated to \(\$ 11,000\) If the car's value continues to drop by the same percentage, what will it be worth by 2017\(?\)

What role does the horizontal asymptote of an exponential function play in telling us about the end behavior of the graph?

What is the advantage of knowing how to recognize transformations of the graph of a parent function algebraically?

For the following exercises, graph the function and its reflection about the \(x\) -axis on the same axes. $$f(x)=3(0.75)^{x}-1$$

For the following exercises, describe the end behavior of the graphs of the functions. $$f(x)=3\left(\frac{1}{2}\right)^{x}-2$$