## Intermediate Algebra: Connecting Concepts through Application

(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 $0$.
(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 $1880$.