Birth and death rates of animal populations typically are not constant, instead, they vary periodically with the passage of seasons. Find P(t) if the population P satisfies the differential equation dP -=(k+b cos 2xt)P, where t is in years and k and b are positive constants. Thus the growth-rate function r(t)=k+ b cos 2xt varies periodically about its mean value k Construct a graph that contrasts the growth dt of this population with one that has the same initial value of P but satisfies the natural growth equation P'=KP (same constant k). How would the two populations compare after the passage of many years?