Question 1171138
In​ 2012, the population of a city was 5.21 million. The exponential growth rate was ​2.86% per year.
a) Find the exponential growth function.
t - time in years, pop in millions
{{{f(t) = 5.21(1.0286)^t}}}
:
​b) Estimate the population of the city in 2018.
t = 6 yrs
{{{f(t) = 5.21(1.0286)^6}}}
f(t) =  5.21 * 1.1843
f(t) = 6.17 million in 2018 (6 yrs)
:
​c) When will the population of the city be 9 ​million?
{{{5.21(1.0286)^t = 9}}}
{{{(1.0286)^t = 9/5.21}}}
{{{(1.0286)^t = 1.727}}}
use common logs here
t*log(1.0286) = log(1.727)
{{{t = log(1.727)/log(1.086)}}}
use your calc
t = 19.37 yrs
:
​d) Find the doubling time.
{{{(1.0286)^t = 2}}}
t = {{{log(2)/log(1.086)}}}
t = 24.59 yrs to double