Question

Suppose the population of a town is 9,800 and is growing 2% each year. a. Write an equation to model the population growth. b. Predict the population after 7 years.

A. y = 9,800 • 1.02x ; about 11,257 people


B. y = 9,800 • 2x ; about 11,257 people


C. y = 9,800 • 2x ; about 1,254,400 people


D. y = 2 • 9,800x ; about 137,200 people

Answer 1

The correct option is A.

Explanation:

The general exponential growth model is defined as

`f(x)=a(1+r)^x`

Where, a is initial value, r is growth rate and x is time.

The initial population of town is 9800 and growth rate is 2%. The population growth model is defined as

`f(x)=9800(1+(2)/(100))^x`

`f(x)=9800(1+0.02)^x`

`f(x)=9800(1.02)^x`

Put x=7 to find the estimated population after 7 years.

`f(x)=9800(1.02)^7`

`f(x)=11257.119543\approx 11257`

Therefore the correct option is A.