In 1859, 24 rabbits were released into the wild in Australia, where they had no natural predators. Their population grew exponentially, doubling every 6 months.

(a) Determine P(t), the function that gives the population at time t, and the differential equation describing the population growth. Let units for t be years.

(b) After how many years, rounded to one digit after the decimal point, did the rabbit population reach 1,000,000?

(c) Determine the rate of population change, in rabbits/year, midway through the third year. (Warning: t is not 3.5, just like the year midway through the 21st century is not 2150.) Round the final answer to 2 digits after the decimal point.