Question

A plumber charges $50 for a service call plus $80 per hour. If she spends no longer than 8 hours a day at any one site, find a linear function that represents her total daily charges C (in dollars) as a function of time t (in hours) spent at any one given location.

Answer 1

Answer:

$C(t)=80t+50, \text{ for }t\leq 8$.

Step-by-step explanation:

Let C represent total daily charges in dollars and t represent time in hours.

We have been given that a plumber charges $50 for a service call plus $80 per hour.  

The amount charged for t hours would be $80t$.

The total amount charged for t hours would be $C(t)=80t+50$.

We are also told that plumber spends no longer than 8 hours a day at any one site, this means that time t have a restriction as:

$t\leq 8$

Therefore, our required cost function would be $C(t)=80t+50, \text{ for }t\leq 8$.