\begin{tabular}{l} Graph the following function and its inverse on the same \\ Cartesian plane. \\ \( f(x)=9^{\mathrm{x}} ; \mathrm{f}^{-1}(\mathrm{x})=\log _{9} \mathrm{x} \) \\ Use the graphing tool to graph the function. \\ \hline Click to \end{tabular}

What is the end behavior of the graph of the exponential function \( f(x)=b^{x} \) when \( 0<b<1 ? \) (1 point) \( f(x) \rightarrow \infty \) as \( x \rightarrow \infty, f(x) \rightarrow 0 \) as \( x \rightarrow-\infty \) \( f(x) \rightarrow 0 \) as \( x \rightarrow \infty, f(x) \rightarrow \infty \) as \( x \rightarrow-\infty \) \( f(x) \rightarrow \infty \) as \( x \rightarrow \infty ; f(x) \rightarrow-\infty \) as \( x \rightarrow 0 \) \( f(x) \rightarrow \infty \) as \( x \rightarrow 0 ; f(x) \rightarrow-\infty \) as \( x \rightarrow-\infty \)

Draw the graph of \( f(x)=\log _{3}(x-3)+4 \)

The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 22000 . (a) Find a function that models the population \( t \) years after \( 2000(t=0 \) for 2000). Hint: Use an exponential function with base \( e \). Your answer is \( P(t)= \)

A wooden artifact from an ancient tomb contains 30 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) years

Which function transforms the translating it up 5 units? (1 point) \( g(x)=-2^{x+5} \) \( g(x)=2^{-x+5} \) \( g(x)=-2^{x}+5 \) \( g(x)=2^{-x}+5 \)