In 1859, Thomas Austin put out 24 wild rabbits on his ranch Barwon Park in Australia. He had gotten them from England and these were the first rabbits in Australia. "The introdcution of a few rabbits could do little harm and might not provide a touch of home, in Addition to a spot of hunting "he wrote. In Australia there were large areas with little vegetation, rabbits had no natural enemies, and with mild winters could rabbits multiply all year round. Ten years after you could shoot or capture two million rabbits in a year, without making any visible effect on the size of the population. Ten years after there were ten million rabbits.

a) Which growth model for populations it is natural to use in this case? Explain why. Write down the differential equation for this growth model. (Note that you can not yet know all the constants. We are going to find them below.)

b) Write down the general solution for this differential equation. Find then the solution that models the development of rabbit population in Australia.

c) What was the doubling time of the rabbit population in Australia during this time period?