Chapter 5.4, Problem 5STP

For Exercises $1-5,$ choose the correct letter.

The population of a city increases by 4000 people each year. In 2025, the population is projected to be 450,000 people. What is an equation that gives the city’s population $p$ (in thousands of people) $x$ years after 2010?

A. $p=4x+450$

C. $p-15=4(x-450)$

B. $p-450=4(x-15)$

D. $p=4x+15$

To determine

To select:The correct equation that gives the city’s population after 2010

Answer to Problem 5STP

B. is the correct option.

Explanation of Solution

Given information:

  $p$ = population (in thousands) $x$ = years after 2010,

Projected population in 2025= 450,000, Population increase every year= 4000

Calculation:

Taking the equation of B. and solving it

  $p-450=4(x-15)$

We know no. of years after 2010 till 2025 is 15, that is, $x$ =15.

Therefore,

  $\begin{array}{l}p-450=4(15-15)\\ \Rightarrow p-450=0\\ \Rightarrow p=450\times {10}^3=450,000\\ \end{array}$ Since, $p$ is in thousands

Thus, the above equation satisfy the given conditions,

Hence option B$p-450=4(x-15)$ is the correct option.