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?

1 Answer
Feb 19, 2016

#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.