Final answer:
The labor cost for repairing a computer at a rate of $50 per hour or part thereof is modeled by a step function, which increases by $50 with each new started hour. The formula to calculate this cost is y = 50 ⋅ ⌊ x ⌋, where x is the number of hours and y is the total labor cost.
Step-by-step explanation:
The type of function that models the labor cost of repairing a computer when the charge is $50 per hour or fraction thereof is a step function. A step function increases in steps, rather than continuously, as each new hour or fraction of an hour of labor is added. For instance, if it takes 1 hour and 10 minutes to repair a computer, the labor cost would be $100 because the charge is $50 for each started hour.
The general formula for calculating the labor cost (y) given the number of hours (x) can be written as:
y = 50 ⋅ ⌊ x ⌋
where ⌊ x ⌋ represents the smallest integer greater than or equal to x (the ceiling function), meaning you round up to the nearest whole hour. For example:
- If it takes 0.5 hours, the cost is $50 (⌊ 0.5 ⌋ = 1).
- If it takes 1.25 hours, the cost is $100 (⌊ 1.25 ⌋ = 2).
- If it takes 2 hours, the cost is $100 (⌊ 2 ⌋ = 2).
Therefore, each partial hour adds an additional $50 to the total labor cost, regardless of how many minutes into the hour you are.