Question

A small country that had 20 million people in 1990 has experienced exponential growth in population of 4% per year since then. How do you write an equation that models this situation and use your equation to determine when the population will double?

Answer 1

`P_x`, the population after `x` years, is given by `20*1.04^x` million and population doubles in `17.67` years.

Explanation:

Population is 20 million people in 1990 and growth in population of 4% per year. Hence, after `x` years population will be

`20(1+4/100)^x` million or `20*1.04^x` million .

Hence, `P_x`, the population after `x` years, is given by `20*1.04^x` million.

If it doubles in x years, `20*1.04^x=40` or `1.04^x=40/20=2`

Hence `x=(log 2)/(log 1.04)=0.30103/0.01703334=17.67` years.