Question

The population of a town decreased from 265000 to 198200 in a decade. What is the average percent decrease of population per year?

Answer 1

Given:

Population 10 years ago = 265000

Population 10 years now = 198200

To Find:

The average percent decrease per year

Solution

$198200 = 265000( 1 + \dfrac{r}{100})^{10}$

$( 1 + \dfrac{r}{100})^{10} = \dfrac{198200}{265000}$

$( 1 + \dfrac{r}{100})^{10} = \dfrac{991}{1325}$

$1 + \dfrac{r}{100} = \sqrt[10]{ \dfrac{991}{1325} }$

$1 + \dfrac{r}{100} = 0.9714$

$\dfrac{r}{100} = 1 - 0.9714$

$\dfrac{r}{100} = 0.0286$

$r = 2.86\%$

Answer: The average percentage decrease per year is 2.86%