# Important information about logistic models

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A population obeys the logistic model. It satisfies the equation

dP/dt = 2/1300 P(13-P) for P>0

Assume P(0)= 3 Find P(74)

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#### Solution Preview

dp

-- = (2*p*(13-p)) / 1300

dt

Using seperation of variables:

dp

------- = (2/1300) * dt

p(13-p)

Note: by partial fractions we can turn 1/p(13-p) into

1/13*p + 1/(13)(13-p) which makes our differential equation

dp dp

---- + --------- ...

#### Solution Summary

This shows how to use the logistic model to solve a function for a given value.

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