The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this...

Question

The population of a new city is 5 million and is growing at 20% annually. How many years would it take to double at this growth rate?

A. 3 - 4 years  B. 4 - 5 years  C. 5 - 6 years  D. 6 - 7 years

Accepted Answer

Doubling occurs between year 3 and year 4, so the answer is 3 - 4 years (Option A). We need to find n such that 5 * (1.2)^n = 10, i.e. (1.2)^n = 2. Since n need not be a whole number, we check successive integer powers of 1.2 to bracket the doubling point. The exact value falls between 3 and 4 years.