calculus q (1 Viewer)

[hannahxxx]

Hey I was just wondering if neone could help me out with this q?
Apparantly the answer is 11.4 yrs. I'm just stuck with the working:

A population in a certain city is growing at a rate proportional to the population itself. After 3 years the population increases by 20%. How long will it take for the population to double?

Cheers

 

[Ennaybur]

no worries

 

[hannahxxx]

Let initial population = P

P = Ae^kt
When t = 0
P = A

First find k
1.2P = Pe^3k
1.2 = e^3k
ln 1.2 = 3k
k = 0.06077

For population to double
2P = Pe^kt
ln 2 = kt
t = 11.4

Lifesaver. Thanks!