# Applications of Calculus

1. May 11, 2010

### 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!

2. May 11, 2010

### 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.

3. May 11, 2010

### Sirsh

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

4. May 11, 2010

### Cyosis

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

5. May 11, 2010

### Sirsh

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

6. May 11, 2010

### 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.