The city of Mississauga has experienced rapid growth in rece

The city of Mississauga has experienced rapid growth in recent years. It had a population of 234975 in 1975 and 610700 in 2000. Determine the annual growth rate of the population over the 1975-2000 period.

Solution

The rate of growth is exponential in nature. This gives the population in year n as P(n) = Po*(1 + r)^n, where Po is the initial population and r is the growth rate.

The population in year 1975 is Po = 234975 and that in year 2000 is 610700.

n = 2000 - 1975 = 25

610700 = 234975*(1+r)^25

=> (1 + r)^25 = 610700/234975

=> [25*log(1+r) = log(610700/234975)]

=> [log(1+r) = 0.01659225]

=> [(1+r) = 10^0.01659225]

=> 1 + r = 1.038944266

=> r = 3.894%

The growth rate over the years 1975 - 2000 is 3.894%