Suppose that a certain population satisfies the initial value problem dy/dt = r(t)y − k, y(0) = y0, where the growth rate r(t) is given by r(t) = (1 + sin t)/5, and k represents the rate of predation. (a) Suppose that k = 1/5. Plot y versus t for several values of y0 between 1/2 and 1. (b) Estimate the critical initial population yc below which the population will become extinct. (c) Choose other values of k and find the corresponding yc for each one. (d) Use the data you have found in parts (b) and (c) to plot yc versus k