Question

A population of a certain city increases exponentially at a rate of 6.5%. Initially, it is 1.50 million. After how many years will the population reach 2.31 million?

6.546
6.643
6.123
6.142

Answer 1

Below in bold.

Explanation:

P = 1.50(1.065)^t where P = population in millions and t = no. of years.

So we have

2.31 = 1.50(1.065)^t

(1.065)^t = 2.31/1.50

Taking logs:

t log 1.065 = log (2.31/1/50)

t = log (2.31/1/50) / log 1.065

= 6.856 years.