Question

Which piecewise function represents the following situation?

A house painter charges $12 per hour for the first 40 hours he works, time and a half for the first 10 hours after that, and double time for all hours after that. He will not work over 70 hours a week.

Answer 1

The last piecewise function

Explanation:

The question is asking which of the piecewise functions is applicable in this situation not a value

Given t is the number of hours the painter will work, with the given data let's see how to arrive at the function

If t ≤ 40 then the rate is $12 per hour = 12t

If t > 40 but ≤ 50 then the first 40 hours are at $12 per hour which will fetch him $480. The remainder hours is (t - 40) which are charged at time and half so that would be 12 x 1.5 x t = 18t. The total earned would be 18t + 480

If > 50 ≤ 70 then
First 40 hours at $12 per hour = $480
Next 10 hours at $18 per hour = $180

Remainder hours = (t - 50) and is charged at double time so that would be 24 (t -50)

Total earned = 480 + 180 + 24(t-50) = 660 +2(t-4 50) or 24(t-50) + 180

So the piecewise function that fits this situation is the last one