Rabbits reproduce two-by-two. Typically a rabbit litter is four bunnies. Includi

Question

Rabbits reproduce two-by-two. Typically a rabbit litter is four bunnies. Including gestation period and caring for young, the average mother has two litters a year. As the rabbit population increases, the birthrate (bunnies/year) also increases. If N is the bunny population, then the growth rate N is given by the equation

dN/dt = 2N

a) If there are originally 2 bunnies of the proper gender, what is the equation N(t) for the future population, where t is in years.

b) How many bunnies will there be after 6.5 years?

Explanation / Answer

dN/N=2dt

Integrating both sides,

ln(N)=2t +C, where C is the constant of integration.

At t=1, N=2, so, C=ln(2)-1

N=e2t+ln(2)-1

(b) N after 6.5 years= N(6.5)= e12+ln(2)

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