Suppose that a community in Idaho currently has a population of 5,000 and will be growing with a doubling time of 13 years. What will its population be in 20 years?
What will its population be in 50 years?
First, you have to find out the annual average growth:
2^(1/13) =1.054766...... - 1 x 100 =5.4766% This is the average annual growth rate.
1.054766^20 x 5,000 = ~14,524 expected population of the town in 20 years.
1.054766^50 x 5,000 =~71,908 expected population of the town in 50 years.
You could also do this way:
20/13 = 1.538462...... This is the number of doublings in 20 years
2^1.538462 x 5,000 =14,524 - projected population in 20 years.
50/13 = 3.8461538.... This is the number of doublings in 50 years.
2^3.8461538 x 5,000 =71,908 - projected population in 50 years.
