Question

The population of a small town is increasing at the rate of 2% per year. The town historian records the population at the end of each year and tracks the growth using the function P.-P.(1+r)"where P, is the population when n = 0, P, is the population in n years and r is the rate of change. In 2010, the population was 6,000. If it continues to increase, what will be the population, to the nearesthundred, in 2020

Answer 1

`\begin{gathered} r=0.02 \\ Po=6,000 \\ \text{year1 =2010} \\ \text{year}2=2020 \\ \text{time}=\text{ 10 years} \\ P=Po(1+r)^t \\ P=6,000(1+0.02)^(10) \\ P=7,314 \\ \text{The population in 2020 wil be }7,314 \end{gathered}`