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
asked 2021-02-26
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.

Answers (1)

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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