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cp255

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## Homework Statement

https://www.physicsforums.com/attachment.php?attachmentid=65556&stc=1&d=1389570667

For those who can not see the screen shot here is the question...

Suppose the population P of rodents satisfies the diff eq dP/dt = kP^2.

Initially there are P(0) = 2 rodents, and their number is increasing at the rate of dP/dt = 1 rodent per month when P = 10. How long does it take for the population to reach 105 rodents.

## Homework Equations

## The Attempt at a Solution

First I found k by substituting in 10 for p and 1 for dp/dt.

1 = k * 10^2

k = 1/100

Then to solve the differential equation I integrated both sides with respect to t.

∫dp/dt * dt = ∫0.01 * p^2 dt

p = 0.01p^2 * t + C

I solved for C and found C = 2.

Solving for t gives

t = 100(p - 2) / p^2

I then plunged in 105 for p and the answer was wrong.

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