# Thread: rate of population growth!

1. ## rate of population growth!

The population P of a town has a rate of change proportional to the difference between P and 15,000. This may be expressed as dP/dt = k(P - 15000), where k = 0.2 and t = time in years. Find the population after one year

here is how I decided to do it. can someone please check?

$P = 15,000 + Ae^{0.2t}$

initially,

$21,000 = 15,000 + Ae^{0.2t}$

$6,000 = Ae^{0}$

$6,000 = A$

$P = 15,000 + 6000e^{0.2t}$

when t = 1

$P = 15,000 + 6000e^{0.2}$

$= 22328$

this is not the answer. the answer is 22,000.

what did i do wrong?

2. Originally Posted by differentiate
The population P of a town has a rate of change proportional to the difference between P and 15,000. This may be expressed as dP/dt = k(P - 15000), where k = 0.2 and t = time in years. Find the population after one year

here is how I decided to do it. can someone please check?

$P = 15,000 + Ae^{0.2t}$

initially,

$21,000 = 15,000 + Ae^{0.2t}$

$6,000 = Ae^{0}$

$6,000 = A$

$P = 15,000 + 6000e^{0.2t}$

when t = 1

$P = 15,000 + 6000e^{0.2}$

$= 22328$

this is not the answer. the answer is 22,000.

what did i do wrong?
Do you have the right initial condition? You didn't specify it in the question...

3. ohh sorry, I forgot. It was:

If the population at the beggining of 1960 was 21,000, find the population after one yaer

4. I can't see anything wrong with your working out, I keep getting the same answer.

5. alright thanks man. The book I'm working on keeps having incorrect answers!