Question

Rework problem 15 in section 2 of Chapter 5 of your textbook about the growing suburb and the declining city using the following data: Assume that the suburb has a population of 686000 and is growing at a rate of 4000 per year. Assume that the city has a population of 942000 and is declining at a rate of 12000 per year.

Answer 1

Answer:

16 years.

Step-by-step explanation:

Please consider the complete question.

Assume that the suburb has a population of 686,000 and is growing at a rate of 4000 per year. Assume that the city has a population of 942,000 and is declining at a rate of 12000 per year. In how many years will the populations of the suburb and the city be equal?

Let x represent number of years.  

Growth function would be $G(x)=4000x+686,000$ and decline function would be $D(x)=942,000-12,000x$.

To find the time when both populations will be equal, we will equate both functions as:

$4000x+686,000=942,000-12,000x$

$4000x+12,000x+686,000=942,000$

$16,000x+686,000=942,000$

$16,000x=942,000-686,000$

$16,000x=256,000$

$\frac{16,000x}{16,000}=\frac{256,000}{16,000}$

$x=16$

Therefore, in 16 years the populations of the suburb and the city will be equal.