Chapter 1, Problem 47RE

A breeding group of $20$ bighorn sheep is released in a protected area in Colorado. It is expected that with careful management the number of sheep, $N,$ after $t$ years will be given by the formula $N=\frac{220}{1+10\left({0.83}^t\right)}$ and that the sheep population will be able to maintain itself without further supervision once the population reaches a size of $80$ .

(a) Graph $N$ versus $t$ .

(b) How many years must the state of Colorado maintain a program to care for the sheep?

(c) How many bighorn sheep can the environment in the protected area support?