How Can We Use Calculus to Predict Population Growth?

[Sirsh]

Hi all, I'm just wondering if this is correct: \frac{dP}{dt} =0.2P If the population is now 5300:
(a) Write a formula for the population in t years time.

To do this would i antidifferntiate 0.2P, so.. (0.2P^2)/2 = 0.1P^2 + t?

Thank you!

 

[Cyosis]

No that is wrong. dP and 0.2P are on opposite sides. Rewrite the equation in such a way that all Ps are on the same side and all ts on the other side.

 

[Sirsh]

dP/0.2P = dt? or dP/P = 0.2dt

 

[Cyosis]

Both are correct. Now you can integrate both sides of that equation.

 

[Sirsh]

Um, Does the equation mean that: the derivative of P divided by P equals 0.2 times the derivative of t?

 

[Cyosis]

No dP=\frac{dP}{dt} dt, but as you can see they are very closely related. Just put the integral sign in front of both sides of the equation and it will become clear what to do.