Urban planners are studying the population changes of a town
MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms
Problem
Urban planners are studying the population changes of a town. The town had 20,000 inhabitants at the end of 1990. For each of the next 12 years (1991–2002) the population increased by 6 % compared with the previous year. From 2003 onward, economic factors caused an annual decrease such that each year's population became exactly 90 % of the preceding year's figure.
(i) Write an expression for the population at the end of the nth year after 1990, clearly distinguishing the two phases of growth and decline.
(ii) Calculate the population at the end of 2002.
(iii) Determine the population at the end of 2007.
(iv) Find the first year after 1990 in which the population becomes less than 15,000.