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A population P obeys the logistic model. It satisfies the equation

https://webwork.math.uga.edu/webwork2_files/tmp/equations/11/02d0a645c053f1f6002d746c78143f1.png

Assume that P(0)=3. Find P(66)

First I multiplied both sides by dt and integrated, giving:

P=6/700Pt(7-P)+c

If P(0)=3 then c=3

P=6/700Pt(7-P)+3

Then I divided everything by P and had

1=6/700t(7/P-1)+3/P

Now to find P(66)

1=6/700*66(7/P-1)+3/P

1=396/700(7/P-1)+3/P

1=2772/700P-396/700+3/P

4872/700P=1096/700

P=4.445

That's not right, what am I missing?

Thanks.

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# Growth problem

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