QCEVault

Differential equations — Question 78

Original QCE Vault practice · 7 marks

Q78 · Practice questionComplex unfamiliar7 marks

QUESTION 78 (7 marks)

A population PP satisfies dPdt=0.3P(1−P500),P(0)=50.\frac{dP}{dt}=0.3P\left(1-\frac P{500}\right),\qquad P(0)=50.
a)
Solve the differential equation for P(t)P(t).
[3 marks]
b)
Determine when P=300P=300, to two decimal places.
[2 marks]
c)
Determine the population at which the instantaneous growth rate is greatest and the corresponding maximum growth rate.
[2 marks]
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