91Ó°ÊÓ

For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. $$ \log _{2}\left(y^{x}\right) $$

Graph the function and its reflection about the y-axis on the same axes, and give the y-intercept. $$f(x)=3\left(\frac{1}{2}\right)^{x}$$

Use the logistic growth model \(f(x)=\frac{150}{1+8 e^{-2 x}}.\) Find and interpret \(f(4)\) . Round to the nearest tenth.

For the following exercises, use the logistic growth model \(f(x)=\frac{150}{1+8 e^{-2 x}}\). Find and interpret \(f(4)\). Round to the nearest tenth.

For the following exercises, rewrite each equation in exponential form. $$\log _{16}(y)=x$$

For the following exercises, graph the function and its reflection about the \(y\) -axis on the same axes, and give the \(y\) -intercept. $$ f(x)=3\left(\frac{1}{2}\right)^{x} $$

For the following exercises, identify whether the statement represents an exponential function. Explain. The height of a projectile at time \(t\) is represented by the function \(h(t)=-4.9 t^{2}+18 t+40\).

Use the logistic growth model \(f(x)=\frac{150}{1+8 e^{-2 x}}.\) Find the carrying capacity.

For the following exercises, consider this scenario: For each year \(t,\) the population of a forest of trees is represented by the function \(A(t)=115(1.025)^{t} .\) In a neighboring forest, the population of the same type of tree is represented by the function \(B(t)=82(1.029)^{t} .\) (Round answers to the nearest whole number.) Which forest's population is growing at a faster rate?

For the following exercises, use the logistic growth model \(f(x)=\frac{150}{1+8 e^{-2 x}}\). Find the carrying capacity.