The park currently contains 20 wolves and the park rangers are introducing additional wolves at the rate mt(12−t) wolves per month, 0≤t≤12

Question

for some constant m>0 to be determined. However, the park rangers are concerned about damaging the current rabbit population. It is estimated that the rate of growth of the rabbit population in the park is given by
r(t)=56+10cos(πt6)−W(t) rabbits per month, 0≤t≤12
where W(t) is the number of wolves in the park at time t.
(a) Write an expression for the function W(t) for 0≤t≤12.
(b) What constant m should the park rangers choose so that the rabbit population is the same at the end of the year as in the beginning of the year?
(c) With the same constant m of part b), what is the average rate at which wolves will be introduced to the park?