Many biological populations, both plant and animal, experience seasonal growth. For example, an animal population might flourish during the spring and summer and die back in the fall. The population, f(t), at time t is often modeled by f(t) = f(0)e^{csin(kt)}, where f(0) is the size of the population when t = 0. Let f(t) be the population of a particular bird species t months after January 1, 2000. Suppose that the population in the year 2000 is 100 birds, c = 3, k = pi/6. a) Find the size of the population on May 1, 2000. b) Find the instantaneous rate of change of the population on May 1, 2000.