Question

Jonesville and smithville each have a population of size 2600 at time t = ​0, where t is measured in years. Suppose jonesville​'s population grows by 170 people per year. Suppose the population of smithville grows by 7​% per year.

1. Which is true? (Circle one)
A. Both towns are growing exponentially.
B. Jonesville is growing linearly and Smithville is growing exponentially.
C. Jo nesville is growing exponentially and Smithville is growing linearly
D. Both towns are growing linearly.

Answer 1

Answer: B. Jonesville is growing linearly and Smithville is growing exponentially.

Explanation:

Linear growth :

• Population grow by a constant amount after each time period.
• The rate of change of dependent variable with respect to independent variable is a constant.
• It is represented by line on graph.
• Equation for linear growth :
  `y=mx+c` , c = initial value and m is the rate of change of y with respect to x.

Exponential growth :

• Population grow by a constant ratio .
• It is represented by a curve on graph.
• Equation for exponential growth :
  `y=a(1+r)^x` , a = initial value and r is rate of growth ( in decimal ) and x is time period.

Given : Jonesville​'s population grows by 170 people per year.

i.e .Population grow by a constant amount per year.

⇒ Jonesville is growing linearly.

The population of smithville grows by 7​% per year.

i.e. Population grow by a constant ratio.

⇒Smithville is growing exponentially.

Hence, the true statement is "B. Jonesville is growing linearly and Smithville is growing exponentially."