# 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.

Question
Exponential growth and decay
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.

2021-02-27
a)population in 2010, $$P_o=3050$$
population in 2015, p=3500
time in years, t=5
use the exponential growth model
$$p=p_o(1+r)^t$$
$$3500=3050(1+r)^5$$
$$(70/61)=(1+r)^5$$
$$(70/61)^(1/5)=1+r$$
r=1.0279-1
r=0.0279
Therefore the growth rate is 0.0279 or 2.79%
b)for 2018,t=8
$$p=p_o(1+r)^t$$
$$=3050(1+0.0279)^8$$
$$approx3801$$
Therefore, the population is 3801 in 2018

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