91Ó°ÊÓ

Each of the following functions is one-to-one. Find the inverse of each function and express it using \(f^{-1}(x)\) notation. $$ f(x)=5 x-1 $$

Find A using the formula \(A=P e^{r t}\) given the following values of \(P, r,\) and \(t .\) Round to the nearest hundredth. $$ P=25,000, r=6.5 \%, t=100 \text { years } $$

Use a graphing calculator to graph each function. Determine whether the function is an increasing or a decreasing function. See Using Your Calculator: Graphing Exponential Functions. $$ f(x)=-3\left(2^{x / 3}\right) $$

Write each logarithmic equation as an exponential equation. See Example 1. Do not solve. $$ \log _{n} C=-42 $$

Each of the following functions is one-to-one. Find the inverse of each function and express it using \(f^{-1}(x)\) notation. $$ f(x)=\frac{x}{5}+\frac{4}{5} $$

Solve each equation. Give the exact solution and an approximation to four decimal places. $$ e^{2.9 x}=4.5 $$

Find A using the formula \(A=P e^{r t}\) given the following values of \(P, r,\) and \(t .\) Round to the nearest hundredth. $$ P=15,895, r=-2 \%, t=16 \text { years } $$

Solve each equation. Give the exact solution and an approximation to four decimal places. $$ e^{3.3 t}=9.1 $$

Find A using the formula \(A=P e^{r t}\) given the following values of \(P, r,\) and \(t .\) Round to the nearest hundredth. $$ P=33,999, r=-4 \%, t=21 \text { years } $$

Use a graphing calculator to graph each function. Determine whether the function is an increasing or a decreasing function. See Using Your Calculator: Graphing Exponential Functions. $$ f(x)=-\frac{1}{4}\left(2^{-x / 2}\right) $$