Solve the equation. Give the actual solution and approximate the solution to four decimal places. See the earlier example.

$$3^x=11$$

Practice using the exponential decay formula by completing the table below. Round final amounts to the nearest whole.

$$\begin{array}{c|c|c|c} \hline \text { Original } & \begin{array}{c} \text { Decay } \\ \text { Rate per } \\ \text { Ymount } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Years, } \boldsymbol{x} \end{array} & \begin{array}{c} \text { Final } \\ \text { Amount } \\ \text { after } \boldsymbol{x} \text { Years } \\ \text { of Decay } \end{array} \\ \hline 402 & 7 \% & 5 & \\ \hline \end{array}$$

Watch the section lecture video and answer the following questions.

From Example 3. given two functions $f(x)$ and $g(x)$, can $f(g(x))$ ever equal $g(f(x))$ ?

Determine whether each function is a one-to-one function. If it is one-to-one, list the inverse function by switching coordinates, or inputs and outputs.

$$\begin{aligned} &\\ &\begin{array}{l|c|c|c|c|c} \hline \text { Srate (Input) } & \text { Texas } & \text { Massachusetts } & \text { Nevada } & \text { Idaho } & \text { Wisconsin } \\ \hline \text { Number of Two-Year Colleges (Output) } & 70 & 22 & 3 & 3 & 31 \\ \hline \end{array} \end{aligned}$$

Find whether the function is a one-to-one function. If it is one-to-one, list the inverse function by switching coordinates, or inputs and outputs. See the earlier example.

$$\begin{array}{l|c|c|c|c|c} \hline \text { State (Input) } & \text { Texas } & \text { Massachusetts } & \text { Nevada } & \text { Idaho } & \text { Wisconsin } \\ \hline \text { Number of Two-Year Colleges (Output) } & 70 & 22 & 3 & 3 & 31 \\ \hline \end{array}$$