Question

A city currently has 153 streetlights. As part of a urban renewal program, the city council has decided to

install 3 additional streetlights at the end of each week for the next 53 weeks.
Find an explicit formula for the number of streetlights after a weeks. Pa = 153 + 3x
How many streetlights will the city have at the end of 33 weeks:

Answer 1

The explicit function is:
`P_x = 153+3x`

And the number of lights after 33 weeks will be 252.

Explanation:

Given that:

Total street lights = 153

Let x be the number of weeks

Then the number lights after x weeks will be 3x

This is a linear function where the y-intercept is 153 and slope is 3.

It can be written as: y = mx+b

The function is:

`P_x = 153+3x`

Putting the values for x will give us the number of total lights after that number of weeks.

To find, how many street lights were there at the end of 33rd week,

Putting x = 33

`P_(33) = 153+ 3(33)\\= 153+99 = 252`

Hence.

The explicit function is:
`P_x = 153+3x`

And the number of lights after 33 weeks will be 252.