Answer
a) $1000$ people in year $0$ and $1480.244$ people in year $10$ .
b) See the plots
c) About $23.36$ years after $t=0$, the population will be $2500$.
Work Step by Step
(a) $f(0)=1000(1.04)^0=1000$, this means there are 1000 people in year 0 . $f(10)=1000(1.04)^{10} \approx 1480.244$, this means there are $1480.244$ people in year $10$.
(b) For the first $10$ years, use $0 \leq t \leq 10,0 \leq P \leq 1500$. See the first figure . For the first 50 years, use $0 \leq t \leq 50$, $0 \leq P \leq 8000$. See the second figure.
(c) The graph of $P(t)$ and $P=2500$ intersect at $t \approx 23.36$. Thus, about $23.36$ years after $t=0$, the population will be $2500$.
