Question

the population of a southern city follows the exponential law. If the population doubled in size over an 18 month period and the current population in 10000, what will be the population 2 years from now?

the equation for the exponential equation is: A=ao e ^ -kt

ao is the original amount

a is what the population will be

t is the amount of time

k is the rate of growth

Answer 1

I don't see why the exponent is negative since this an exponentional growth, the negative usually indicates decay.

Anyway...
I would use A = a (e^kt), where t is months
using << the population doubled in size over an 18 month period >>
2 = 1(e^18k)
ln 2 = 18k
k = ln 2/18

so A = 1000 (e^(24*ln2/18))
= 1000(2.51984)
= 2520

another way would be to use

A = 1000(2)t/k and put in t=24
A = 1000(2^1.3333333)
= 2520