How fast is the population growing at the moment it reaches 75,000?

Explanation

1. 01

   $P'(t) = 0.02 \times 50{,}000\,e^{0.02t} = 0.02\,P(t)$: the rate is 0.02 times the population.

2. 02

   When $P = 75{,}000$: $0.02 \times 75{,}000 = 1500$ people per year.