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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 312

The population P P\,P of a colony is measured in thousands and time t t\,t is measured in years. Without intervention, the rate of increase of the population is proportional to PPP. When P=4P=4P=4, the population is increasing at 0.12 thousand per year.

a.

Construct a differential equation for P P\,P in the form

dPdt=kP\dfrac{dP}{dt}=kPdtdP​=kP,

and find kkk.

The colony is then harvested continuously at a constant rate of 0.10 thousand per year.

[3]
b.

Construct the new differential equation.

[2]
c.

According to this model, determine the range of values of P P\,P for which the population is decreasing.

[2]
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3 Unit A2 1: Pure Mathematics (A-level only) Questions

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