Question

A town’s population has been decreasing at a constant rate. In 2010 the population was 5,900. By 2012 the population had dropped to 4,700 people. Assume this trend continues.The population in 2016 will be Answer people.

Answer 1

2,300 people.

Step-by-step explanation:

The sentence "decreasing at a constant rate" suggests a linear relationship.

• The population in 2010 = 5900 =>(0, 5900)

,

• The population in 2012= 4700 =>(2, 4700)

First, determine the constant rate of the population's decrease.

`\text{Rate}=(5900-4700)/(0-2)=(1200)/(-2)=-600`

Thus, we can model the town's population using the linear function.

`y=5900-600x`

In 2016, that is, 6 years after 2010: x=6

`y=5900-600(6)=5900-3600=2300`

The population in 2016 will be 2,300 people.