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2. Consider a rabbit population P(t) satisfying fraction numerator d P over denominator d t end fraction equals a P minus b P squared where B equals a P is the rate at which births occur and D equals b P squared is the rate at which deaths occur. Suppose the initial population is 240 rabbits and there are 6 births per month and 12 deaths per month occurring at time t=0. a. Solve for a,b. b. Rewrite the differential equation with these values and in the form fraction numerator d P over denominator d t end fraction equals k P left parenthesis M minus P right parenthesis. c. For initial value P left parenthesis 0 right parenthesis equals P subscript 0, the IVP has solution P left parenthesis t right parenthesis equals fraction numerator M P subscript 0 over denominator P subscript 0 plus left parenthesis M minus P subscript 0 right parenthesis e to the power of negative k M t end exponent end fraction.