The time rate of change of a rabbit population is proportional to P^(3/2) . At time t= 0 days, the population numbers 100 rabbits and is increasing at the rate of 2 rabbits per day. (a) Find the population P as a function of t, the number of days elapsed. (b) To the nearest day, how long will it be before the population numbers 300 rabbits? (c) What is the long-term outlook for this population? Will the number of rabbits ultimately stabilize (if so, at what level)? Will there be a population explosion (if so, when)? Will the rabbits become extinct? Explain.

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