Respuesta :
Given:
The number of streetlights in a town is growing linearly
Let the number of streetlights = p
And the months = m
so,
[tex]p=k\cdot m+c[/tex]There were 143 lights 8 months ago; now there are 162 lights.
So, c = 143, m = 8, p = 162
So,
[tex]\begin{gathered} 162=8k+143 \\ 8k=19 \\ k=\frac{19}{8} \end{gathered}[/tex]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:
[tex]p=\frac{19}{8}m+143[/tex]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:
[tex]p=\frac{19}{8}\cdot12+143=171.5[/tex]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
[tex]\begin{gathered} 240=\frac{19}{8}m+143 \\ 240-143=\frac{19}{8}m \\ 97=\frac{19}{8}m \\ m=97\cdot\frac{8}{19}=40.84 \end{gathered}[/tex]Rounding to the nearest whole number
So, the number of months = 41
