Suppose there is a country in which 40% of people are below age 20, 40% are between ages 20 and 40, and 20% are between ages 40 and 60. Assume no one lives above age 60 and the fertility rate is 4. The initial population size is 100.

a. Compute the proportion of young, adult, and old after 20, 40, 60, 80, and 100 years.
b. Calculate the population growth rate over each period of 20 years.
c. Assume a country with the same population composition but with a fertility rate of 2 as a consequence of family planning policies. Do the same exercise as in (a) and (b) above. What is the effect of family planning policies after 20, 40, 60, 80, and 100 years on i) population growth and ii) the composition of the population.