# rate of population growth!

• Sep 25th 2009, 11:41 PM
differentiate
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?

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

initially,

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

\$\displaystyle 6,000 = Ae^{0}\$

\$\displaystyle 6,000 = A \$

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

when t = 1

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

\$\displaystyle = 22328\$

what did i do wrong?
• Sep 25th 2009, 11:53 PM
Prove It
Quote:

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?

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

initially,

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

\$\displaystyle 6,000 = Ae^{0}\$

\$\displaystyle 6,000 = A \$

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

when t = 1

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

\$\displaystyle = 22328\$

what did i do wrong?

Do you have the right initial condition? You didn't specify it in the question...
• Sep 26th 2009, 12:04 AM
differentiate
ohh sorry, I forgot. It was:

If the population at the beggining of 1960 was 21,000, find the population after one yaer
• Sep 26th 2009, 12:40 AM
Prove It
I can't see anything wrong with your working out, I keep getting the same answer.
• Sep 26th 2009, 01:31 AM
differentiate
alright thanks man. The book I'm working on keeps having incorrect answers! :(