Doubling Time Formula

Question

Assume the population of a local village grows at an annual rate of 4.5%.

Using the Rule of 70, calculate approximately how long before the village has doubled in population?

(Round to the nearest tenth.)

 If a village has about 240 people, approximately how many people will there be in 9 years?

(Round to the nearest whole number.)

Answer 1

1. The rule of 70 says that the growth rate in % per some amount of time, times the number of periods of that amount of time, equals approximately 70.

 

For example, if a bank account is giving around 1% annual interest per year, it would take around 70 years for the money in the account to double.

 

So in this case, the population growth rate is 4.5% per year.  To find the number of years it would take for the population to double, divide 70 by 4.5.  The result is 15.555.... so the answer to the nearest tenth is 15.6 years.

 

2. To find the population after 9 years, you have to apply 9 years of compounded growth at the rate of 4.5% per year.  The formula for this is A(1+r)ⁿ, where A is the starting number, r is the growth rate, and n is the number of periods.

 

So the number after 9 years is 240(1+4.5%)⁹ = 240(1.045)⁹ = approximately 356.66.  Rounded to the nearest whole number, that's 357.