fundamental theorem of calc 2

Question

the population of a town is increasing at a rate given by  

P′(t)=33e0.012t​,

where P is the population t years after the beginning of 1990. If the population at the

beginning of 1990 was

5200​,

then estimate the population at the beginning of the year 2020.

ROUND TO THE NEAREST

PERSON.

The population at the beginning of 2020​ is/was about

enter your response here.

Answer 1

P(t)=∫33e^0.012tdt = (33/0.012)e^0.012t+C = 2750e^0.012t+C

P(0) = 5200 = 2750+C

C = 2450

P(t) = 2750e^0.012t+2450

P(2020-1990) = 2750e^0.012(30)+2450 ≈ 6392