# The population of a rural community was 3050 in 2010 and the population had increased to 3500 in 2015. Assuming exponential growth find the following. a. The growth rate to 4 decimal places and as a percentage. b. Estimate the population in 2018 if the trend continues.

The population of a rural community was 3050 in 2010 and the population had increased to 3500 in 2015. Assuming exponential growth find the following.
a. The growth rate to 4 decimal places and as a percentage.
b. Estimate the population in 2018 if the trend continues.
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Demi-Leigh Barrera

a)population in 2010, ${P}_{o}=3050$
population in 2015, p=3500
time in years, t=5
use the exponential growth model
$p={p}_{o}\left(1+r{\right)}^{t}$
$3500=3050\left(1+r{\right)}^{5}$
$\frac{70}{61}=\left(1+r{\right)}^{5}$
${\frac{70}{61}}^{\frac{1}{5}}=1+r$
$r=1.0279-1$
$r=0.0279$
Therefore the growth rate is 0.0279 or 2.79%
b)for 2018,t=8
$p={p}_{o}\left(1+r{\right)}^{t}$
$=3050\left(1+0.0279{\right)}^{8}$
$\approx 3801$
Therefore, the population is 3801 in 2018