Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end
-A herd of moose is introduced to a wildlife refuge. The number of moose, $N ( t )$, after $t$ years is described by the polynomial function $N ( t ) = - t ^ { 3 } + 25 t + 120$. 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 die out.
B) The moose population in the refuge will grow out of control.
C) The moose population in the refuge will reach a constant amount greater than 0 .
D) The moose population in the refuge will be displaced by "oil" wells.

Question

Quizplus · Accepted Answer

The leading term of the polynomial $N(t) = -t^3 + 25t + 120$ 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 (as is the case here), the function's values will decrease without bound as $t$ increases. This implies that the moose population will eventually decrease towards zero, suggesting the population will die out.

Use the Leading Coefficient Test to Determine the End Behavior N(t)N ( t )N(t)

Use the Leading Coefficient Test to Determine the End Behavior $N ( t )$