Algebra and Trigonometry and Their Applications

Math 148 Autumn Quarter, 2001

Instructor: Sergei Chmutov

Bonus problem. Wildlife Management
10 points extra credit

A herd of 122 white-tailed deer is introduced to a coastal island where there had been no deer before. Their population is predicted to increase according to the formula:

\begin{displaymath}N={5984\over 32 + 17e^{-0.12t}}\ ,\end{displaymath}

where $N$ is the number of deer expected in the heard after $t$ years.

(A) How many deer will be presented after 3 years? After 7 years?

(B) How many years will it take for heard to grow to 150 deer? Find the explicit formula for the number of years using logarithms. Compute the approximate number of years from that formula using calculator (round answer to nearest integer).

(C) Does $N$ approach a limiting value as $t$ increases without bound? Explain.