In 2012 the population of a city was 6.84 million the exponential growth rate was 2.85% per year

Question

Find the exponential growth function

estimate the population of the city in 2018

when will the population of the city be 9 million

find the doubling time

Answer 1

P = 6.84e^.0285t where t = the year minus 2012

P = 6.84e^.0285(6) = population in 2018

=6.84e^.171 = 8,115,597 in 2018

9 = 6.84e^.0285t

9/6.84 = e^.0285t

.274437= .0285t

t = 9.63 years = about 9 years 7 1/2 months to reach 9 million population, the year 2022

2 = e^.0285t take natural logs of both sides

ln2 = .0285t divide by 0.0285

t = ln2/0.0285 = about 24.32 years to double the population