Neco Model Questions Vol1 2018 Economics Question 10

The population of a country in the year 2020 is 20 million. Population growth follows a logistic model with carrying capacity \(K = 50\) million. From 2020 to 2030 the intrinsic growth rate is constant at \(r = 0.03\) per year. Beginning in 2031 the rate declines linearly by 0.001 each year until it reaches 0.015 in 2045, after which it stays at 0.015. (a) Write the logistic solution for the period 2020‑2030 and compute the population at the end of 2030 (to two decimal places). (b) Using the yearly varying rates, set up the discrete recursion \(P_{t+1}=P_t+r_t P_t\left(1-\frac{P_t}{K}\right)\) and compute the population in 2050. Give the 2050 population rounded to the nearest thousand. (c) The proportion of the population that is of working age (15‑64) is given by \(W = 0.6 - 0.001\,(P-20)\), where \(P\) is the population in millions. Compute the dependency ratio (number of dependents per 100 working‑age persons) in 2050, rounded to the nearest whole number.