A population of bighorn sheep: There is an effort in Colorado to restore the population of bighorn sheep. Let N = N (t) denote the number of sheep in a certain protected area at time t.
a. Explain the meaning of 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 favorable for bighorn sheep. What would you expect to be true about the sign of dN dt during this period?
c. This summer a number of dead sheep were discovered, and all 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 dN dt ?
d. If the reintroduction program goes well, then the population of bighorn sheep will grow to the size the available food supply can support and will remain at about that same level. What would you expect to be true of dN dt when this happens?
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