The relative growth rate of a population P(t) of koalas is given in the graph be

Question

The relative growth rate of a population P(t) of koalas is given in the graph below,

where t is years since 1900. Use this information to nd the perecentage increase (or decrease) in

koala population between 1900 and 1960. (You must explain in complete detail why the integral

you take is equal to what you say it is: justify every step!)

The relative growth rate of a population P(t) of koalas is given in the graph below, where t is years since 1900. Use this information to nd the percentage increase (or decrease) in koala population between 1900 and 1960.

Explanation / Answer

integral of dP/dt/P dt = integral of dP/P = ln(Pf/Pi)

integral of P'/P dt = 20*-0.02 + 20*-0.02/2 + 40*0.02/2=-0.2

so Pf/Pi = e^(-0.2)

percentage change = (Pf-Pi)/Pi = Pf/Pi -1 = e^(-0.2)-1=-0.181

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