Chapter 4, Problem 90RE

A lake is stocked with bass by the U.S. Park Service. The population of bass is given by $P\left(t\right)=\frac{3000}{1+2e^{-0.37t}}$, where t is the time in years after the lake was stocked.

a. Evaluate $P\left(0\right)$ and interpret its meaning in the context of this problem.

b. Use the function to predict the bass population 2 yr after being stocked. Round to the nearest whole unit.

c. Use the function to predict the bass population 4 yr after being stocked.

d. Determine the number of years required for the bass population to reach 2800. Round to the nearest year.

e. What value will the term $\frac{2}{e^{0.37t}}$ approach as $t\to \infty$.

f. Determine the limiting value of $P\left(t\right)$.