Question

Write a function rule to model the cost of having a plumber come to fix a broken pipe. Then evaluate for the given number. Roto-Rooter charges $45 for the first hour then $20 an hour after that. Find the cost if it takes 5 hours to fix the broken pipe.

a. C(h) = 20h + 45, C(5) = $145
b. C(h) = 45h + 20, C(5) = $145
c. C(h) = 45 + 20h, C(5) = $145
d. C(h) = 20 + 45h, C(5) = $145

Answer 1

The correct function rule to model the cost of hiring a plumber from Roto-Rooter is C(h) = 45 + 20h, and the total cost for 5 hours of work is $145.

Step-by-step explanation:

To model the cost of hiring a plumber from Roto-Rooter, where the company charges $45 for the first hour and then $20 for each subsequent hour, we can write a function that includes a fixed cost and a variable cost scaled by the number of hours. The correct function would be C(h) = 45 + 20h. For the first hour, you pay the fixed cost of $45, and for each additional hour, you add $20 times the number of hours beyond the first.

To find the cost if it takes 5 hours to fix the broken pipe, you would plug in 5 for h in the function, resulting in C(5) = 45 + 20(5). You calculate the variable cost 20(5) which is $100 and add the fixed cost $45 to get the total cost, C(5) = $145.