Chapter 6.2, Problem 13E

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

A Population of Bighorn Sheep There is an effort in Colorado to restore the population of bighorn sheep. Let $N=N\left(t\right)$ denote the number of sheep in a certain protected area at time t.

a. Explain the meaning of $\frac{dN}{dt}$ in practical terms.

b. A small breeding population of bighorn sheep is initially introduced into the protected area. Food is plentiful, and conditions are generally favor-able for bighorn sheep. What would you expect to be true about the sign of $\frac{dN}{dt}$ during this period?

c. This summer a number of dead sheep were discovered, and all of them were infected with a disease that is known to spread rapidly among bighorn sheep and is nearly always fatal. How would you expect an unchecked spread of this disease to affect $\frac{dN}{dt}$?

d. If the reintroduction program goes well, then the population of bighorn sheep will grow to the site that the available food supply can support and will remain at about that same level. What would you expect to be true of $\frac{dN}{dt}$ when this happens?