Chapter 7.7, Problem 26PPS

To determine

The population of the District of Columbia.

Answer to Problem 26PPS

The population of the District of Columbia is 80,372.

Explanation of Solution

Given:

The population of the District of Columbia is 530,000 in 2010 and decreasing at an average of 0.9%

Concept used:

The formula of increases rate over a time period is given by,

  $\begin{array}{l}F=A{\left(1-r\right)}^n\\ \text{Here,}A\text{is}\text{the population in 2010}\\ \text{Here,}F\text{is}\text{the population in 2030}\\ r\text{is the percentage decreased}\\ n\text{ is the number of years}\end{array}$

Calculation:

The car amount after 6 years is calculated as,

  $\begin{array}{c}F=530,000{\left(1-0.09\right)}^{20}\\ =530,000{\left(0.91\right)}^{20}\\ =530,000\left(0.1516\right)\\ =80,371.80\\ \approx 80,372\end{array}$

As the amount after 6 years of the car will be 5774.60 and Manuel is paying $4500 so if he sold the car at that rate then he will have a loss of $1274

Conclusion:.

Hence, the population of the District of Columbia is 80,372.