Answer
(a) The $P$-intercept is $4934$, which means that the population in Minnesota in the year $2000$ was around $4,934,000$
(b) The $t$-intercept is $-\frac{4934}{41}\approx -120$, which means that the population in Minnesota $121$ years before the year $2000$, which was in $1880$, was $0$.
Work Step by Step
(a) The $P$-intercept can be found by setting $t=0$. Thus, the $P$-intercept is:
\begin{align*}
P&=41t+4934\\
P&=41(0)+4934\\
P&=0+4934\\
P&=4934
\end{align*}
The $P$-intercept is $4394$. This means that in the year $2000$, there were $4,934,000$ people in Minnesota.
(b) The $t$-intercept can be found by setting $P=0$. Thus, the $t$-intercept is:
\begin{align*}
P&=41t+4934\\
0&=41(t)+4934\\
-4934&=41t\\
-\frac{4934}{41}&=t\\
t&\approx -120
\end{align*}
The $t$-intercept is $-\frac{4934}{41}$ or approximately $-120$. This means that the population in Minnesota was $0$ approximately $121$ years ago or in the year $1880$.
