Math help please?

Question

In 2012, the population of a city was 6.14 million The exponential growth rate was 3.53% per year

a) Find the exponential growth function

b) Estimate the population of the city in 2018

c) When will the population of the city be 9 million?

d) Find the doubling time.

Answer 1

a) A=Pe^rt

given r=0.0353 and P(initial population)=6.14

A=6.14e^0.0353t

b)from 2012 to 2018 our t=6

A=6.14e^0.0353(6)=7.59 million

c) final population 9 million means our A=9

9=6.14e^0.0353t (solving for t)

9/6.14=e^0.0353t

ln(9/6.14)=ln(e^0.0353t)

0.3824=0.0353t (log property applied)

0.3824/0.0353=t

t=10.8 approximately in 11 years the population will be 9million

d)A=6.14e^0.0353t (doubling time is referring to doubled population, A=2x6.14)

12.28=6.14e^0.0353t

2=e^0.0353t

ln(2)=ln(e^0.0353t)

ln(2)=0.0353t

ln(2)/0.0353=t

t=19.6 approximately 20 years is out doubling time (if asked to round to the nearest year, if not then keep the decimal value)