A herd of 100 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose the number of deer, N(t), after t years is described by the polynomial function: N(t)+ -t^4 +21t^2 +100, where t0.

Question

A herd of 100 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose the number of deer, N(t), after t years is described by the polynomial function: N(t)+ -t^4 +21t^2 +100, where t>0.

a) use the leading coefficent test to determine the graph's end behavior to the right.

b.) Use the rational zero test to determine the zeros. When will they extinct?

c.) what are the values of t for which N(t) >0

d.) What year does the population decline?

Steve · Answer

(a) even power, negative coefficient means heading down on both sides.

(b) what are the factors of 100?

(c) between 1st two real roots and the last two roots. Or, between the two real roots of there are only two.

(d) do you have calculus to use?
N declines where N' < 0.

Use what you know about the general shape of quartics to guide you along the way.