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
dt

=(k+bcos2πt)P
where t is in years and k and b are positive constants. Thus the growth-rate function r(t)=k+bcos2πt varies periodically about its mean value k. Construct a graph that contrasts the growth of this population with one that has the same initial value P0 but satisfies the natural growth equation P0=kP (same constant k). How would the two populations compare after the passage of many years?