Question

a town has a population of 8400 in 1990. Fifteen years later, it's population had grown to 12 500. Assuming that the population continues to grow at the same exponential rate, when will the population reach 20 000?

Please help im trying to answer this question for past 2 hours

Answer 1

it grew by a factor of 125/84 = 1.488 in 15 years. That is an annual rate of 1.488^(1/15) = 1.02685

So, if t is the number of years after 1990, the population can be found using

P(t) = 8400 * 1.02685^t

To find when P(t) will be 20000, just solve for t in

8400 * 1.02685^t = 20000
1.02685^t = 2.38095
t = log(2.38095)/log(1.02685) = 32.74

So, in the 33rd year after 1990 -- 2023 -- the population will reach 20000

Answer 2

Thanks a lot.

Answer 3

yeeet