Neco Model Questions Vol1 2019 Economics Question 15

A country's population follows the logistic model \(P(t)=\dfrac{K}{1+ae^{-bt}}\) where \(K=50\) million, \(a=4\) and \(b=0.03\) (t in years, \(t=0\) corresponds to 2020). In 2020 the age structure is 30\% (0‑14 years), 60\% (15‑64 years) and 10\% (65+ years) and is assumed to remain proportionally constant as the population grows.\n(a) Estimate the total population in 2030.\n(b) Compute the dependency ratio (young + old over working‑age) in 2030.\n(c) The government wants the dependency ratio to stay below 55\%. If it can reduce the effective carrying capacity to 45 million from the year it starts a new policy, determine the latest whole year by which the policy must be introduced so that the population never exceeds 45 million. Assume the same logistic parameters after the policy is implemented.