Solve the problem
-A herd of moose is introduced to a wildlife refuge. The number of moose, $\mathrm { N } ( \mathrm { t } )$, after $\mathrm { t }$ years is described by the polynomial function $N ( t ) = - t ^ { 3 } + 24 t + 80$. Use the Leading Coefficient Test to determine the graph's end behavior. What does this mean about what will eventually happen to the moose population?
A) The moose population in the refuge will grow out of control.
B) The moose population in the refuge will reach a constant amount greater than 0 .
C) The moose population in the refuge will be displaced by "oil" wells.
D) The moose population in the refuge will die out.

Question

Quizplus · Accepted Answer

The leading term of the polynomial $N(t) = -t^3 + 24t + 80$ is $-t^3$, which has a negative coefficient. According to the Leading Coefficient Test, if the leading term of a polynomial function has a negative coefficient and an odd degree (in this case, 3), the function's values will decrease without bound as $t$ increases. This implies that the moose population will eventually decrease to 0, meaning the population will die out.

Solve the Problem -A Herd of Moose Is Introduced to a Wildlife

Solve the Problem
-A Herd of Moose Is Introduced to a Wildlife