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:

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absor201 absor201 · Answer 1 · 2020-12-08T17:20:34+01:00

Answer:

The explicit function is: [tex]P_x = 153+3x[/tex]

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

Step-by-step 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:

[tex]P_x = 153+3x[/tex]

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

[tex]P_{33} = 153+ 3(33)\\= 153+99 = 252[/tex]

Hence.

The explicit function is: [tex]P_x = 153+3x[/tex]

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