The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 24200 . (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 \( P(t)= \) (b) Use the function from part (a) to estimate the fox population in the year 2008 . Your answer is (the answer must be an integer)

Oiven: \( f(x)=\frac{3}{x-2} \) and \( g(x)=3^{-1} \), Explain why \( f(x)=g(x) \) will have only ONE root. Motivate your answer.

\( f(x)=3 e^{x+1} \), for \( x=-4 \) Your answer is \( f(-4)=\square \)

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

The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 24200 . (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 \( P(t)= \) (b) Use the function from part (a) to estimate the fox population in the year 2008 . Your answer is (the answer must be an integer)

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