A worker gets 22 dollars per hour for a normal work week of 40 hours and time-and-a-half for overtime. Assuming he works at least 40 hours a week, construct a function describing his weekly paycheck, Upper P, as a function of the number of hours worked, t.
My answer: 880+11(t-40)
22*40=880
It says my answer is wrong please help!
Your equation shows him just getting 1/2 time for extra hours. For time and a half, you need
P(t) = 880 + 22*1.5(t-40)
= 880 + 33(t-40)
To construct a function describing the worker's weekly paycheck, there are a few things to consider. First, the worker earns their regular hourly rate of $22 per hour for the first 40 hours worked in a week (the normal work week). For any hours worked beyond 40, the worker earns time-and-a-half, which is $22 * 1.5 = $33 per hour.
Now, let's break down the calculation step by step:
1. Determine the number of regular hours (up to 40 hours) worked in the week:
- If t (the number of hours worked) is less than or equal to 40, the number of regular hours worked is simply t.
2. Determine the number of overtime hours (beyond 40 hours) worked in the week:
- If t is greater than 40, the number of overtime hours worked is calculated as t - 40.
3. Calculate the paycheck for the regular hours:
- Multiply the number of regular hours (step 1) by the regular hourly rate ($22).
4. Calculate the paycheck for the overtime hours:
- Multiply the number of overtime hours (step 2) by the overtime hourly rate ($33).
5. Add the pay for regular hours (step 3) and the pay for overtime hours (step 4) to get the total paycheck, Upper P.
Based on this breakdown, let's construct the function for the worker's weekly paycheck, Upper P, as a function of the number of hours worked, t:
If t ≤ 40:
Upper P(t) = 22 * t
If t > 40:
Upper P(t) = 22 * 40 + 33 * (t - 40)
So, your answer should be:
Upper P(t) = 22 * 40 + 33 * (t - 40)
Let's double-check your example:
If the worker works exactly 40 hours:
Upper P(40) = 22 * 40 = 880.
If the worker works 45 hours:
Upper P(45) = 22 * 40 + 33 * (45 - 40) = 880 + 33 * 5 = 880 + 165 = 1045.
It seems like your initial answer was correct, and the function should be Upper P(t) = 22 * 40 + 33 * (t - 40).