Answer
It is not appropriate to use the model for long term predictions.
Work Step by Step
We are given the function:
$$P(t)=0.138t^4-6.24t^3+86.8t^2-239t+1450,t\geq 0.$$
Since $t$ is the number of years after $1980$, the year $2010$ corresponds to $t=2010-1980=30$.
We use the function $P$ to determine $P(30)$:
$$\begin{align*}
P(30)&=0.138(30^4)-6.24(30^3)+86.8(30^2)-239(30)+1450\\
&=15,700.
\end{align*}$$
An increase from $1450$ to $15,700$ quarterly periodicals in $30$ years seems hardly possible. The model can be used on a shorter period of time ($10-15$ years) because the market was different in $2010$ than it was around $1980-1990$. If we consider only the internet impact, we realize that new factors led to major changes in the market.
