math question's

Question

A city's population is currently 500,000. If the population doubles every 55 years, what will the population be 110 years from now?

Answer 1

2 million in 110 years

in 55 years the population will double from half million to one million

in another 55 years the population will double again, from one million to 2 million.

2 = e^55r

ln2 = 55r

r= ln2/55 = 0.0126 = 1.26% = annual rate of growth

P = Ae^rt with A = original population at time t=0, measured in 100,000's t measured in years

= 5e^110(.0126)

=5e^1.386

= 5(4) = 20

Population after 110 years = 4x500,000 = 2,000,000