91Ó°ÊÓ

In Exercises 15–22, tell whether the function represents exponential growth or exponential decay. Then graph the function. $$ y=0.5 e^x $$

You cook a turkey until the internal temperature reaches \(180^{\circ} \mathrm{F}\). The turkey is placed on the table until the internal temperature reaches \(100^{\circ} \mathrm{F}\) and it can be carved. When the room temperature is \(72^{\circ} \mathrm{F}\), the cooling rate of the turkey is \(r=0.067\). How long do you have to wait until you can carve the turkey?

Expand the logarithmic expression. (See Example 2.) $$\log _5 \sqrt[3]{x^2 y}$$

Evaluate the logarithm. \(\log _{1 / 2} 1\)

In Exercises 15–22, tell whether the function represents exponential growth or exponential decay. Then graph the function. $$ y=0.25 e^{-3 x} $$

The table shows the numbers \(y\) of visits to a website during the \(x\) th month. Write a function that models the data. Then use your model to predict the number of visits after 1 year. $$ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \boldsymbol{x} & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \boldsymbol{y} & 22 & 39 & 70 & 126 & 227 & 408 & 735 \\ \hline \end{array} $$

Describe the transformation of \(f\) represented by \(g\). Then graph each function. \(f(x)=4^x, g(x)=4^{0.5 x-5}\)

In Exercises 15–22, tell whether the function represents exponential growth or exponential decay. Then graph the function. $$ y=0.4 e^{-0.25 x} $$

Evaluate the logarithm. \(\log _5 \frac{1}{625}\)

Determine whether the data show an exponential relationship. Then write a function that models the data. $$ \begin{array}{|c|c|c|c|c|c|} \hline \boldsymbol{x} & 1 & 6 & 11 & 16 & 21 \\ \hline \boldsymbol{y} & 12 & 28 & 76 & 190 & 450 \\ \hline \end{array} $$