Question

If the population of a country is growing at a rate of 2.2% compounded

annually, how long will it take the population of 60,000 people to double?

PLEASE SHOW YOUR WORK!!!!!!

Answer 1

It will take 31.9 years.

The general form of this equation is

y = a(1+r)ˣ, where y is the total population, a is the initial population, r is the growth rate as a decimal number, and x is the amount of time. For our problem, we have

120000 = 60000(1+0.022)ˣ

[The 120,000 is because we are doubling the 60,000 population]

Dividing both sides by 60,000,

120000/60000 = 60000(1+0.022)ˣ/60000
2 = 1.022ˣ

Using logarithms to solve this, we have

`log_(1.022)2=x \\ \\31.85=x \\ \\31.9\approx x`