Chapter 1.1, Problem 11E

Reminder Round all answers to two decimal places unless otherwise indicated.

Note Some of the formulas below use the special number $e$, which was presented in the Prologue.

A Population of Deer When a breeding group of animals is introduced into a restricted area such as a wildlife reserve, the population can be expected to grow rapidly at first, but to level out when the population grows to near the maximum that the environment can support. Such growth is known as logistic population growth, and ecologists sometimes use a formula to describe it. The number N of deer present at time 1 (measured in years since the herd was introduced) on a certain wildlife reserve has been determined by ecologists to be given by the function

$N=\frac{12.36}{0.03+{0.55}^t}$

Figure(1)

a. How many deer were initially on the reserve?

b. Calculate $N\left(10\right)$ and explain the meaning of the number you have calculated.

c. Express the number of deer present after 15 years using functional notation, and then calculate it.

d. How much increase in the deer population do you expect from the $10\text{th}$ to the $15\text{th}$ year?