Question

The number of streetlights in a town is growing linearly. There were 143 lights 8 months ago; now there are 162 lights.(a) Write a linear model to describe the number of streetlights in the town over time, using months as the unit of time.Pt =(b) How many streetlights are expected a year from now? Round your answer to the nearest whole number.lights(c) When do you expect the number of streetlights to reach 240? Round your answer to the nearest month.After months

Answer 1

Given:

The number of streetlights in a town is growing linearly

Let the number of streetlights = p

And the months = m

so,

`p=k\cdot m+c`

There were 143 lights 8 months ago; now there are 162 lights.

So, c = 143, m = 8, p = 162

So,

`\begin{gathered} 162=8k+143 \\ 8k=19 \\ k=(19)/(8) \end{gathered}`

a) Write a linear model to describe the number of streetlights in the town over time, using months as the unit of time.

The linear model will be:

`p=(19)/(8)m+143`

b) How many streetlights are expected a year from now? Round your answer to the nearest whole number.

So, m = 12

Substitute with m into the equation:

`p=(19)/(8)\cdot12+143=171.5`

Rounding to the nearest whole number

So, p = 172

(c) When do you expect the number of streetlights to reach 240?

So, p = 240

Substitute with p to find m

`\begin{gathered} 240=(19)/(8)m+143 \\ 240-143=(19)/(8)m \\ 97=(19)/(8)m \\ m=97\cdot(8)/(19)=40.84 \end{gathered}`

Rounding to the nearest whole number

So, the number of months = 41