Answer
$P(t)\rightarrow +\infty\text{ when }t\rightarrow -\infty$
$P(t)\rightarrow +\infty\text{ when }t\rightarrow +\infty$
Work Step by Step
We are given the function:
$$P(t)=0.138t^4-6.24t^3+86.8t^2-239t+1450,t\geq 0.$$
The polynomial has an even degree, therefore its behavior at $-\infty$ and $\infty$ is the same and depends on the sign of the leading coefficient. Because the leading coefficient is positive, it follows that
$$\begin{align*}
P(t)&\rightarrow +\infty\text{ when }t\rightarrow -\infty\\
P(t)&\rightarrow +\infty\text{ when }t\rightarrow +\infty.
\end{align*}$$
But the domain of the function is $[0,\infty)$, so the graph of the function starts from the point $(0,1450)$.
