Question

1. a plumber’s fee schedule can be modeled with a linear function using his service charge to come to your house and his hourly rate for fixing the problem. the fee schedule for j&b plumbers is $c(h)=$50+$20h$, where $h$ represents the number of hours that the plumber works at your house. (a) what is the service charge (initial value) at j&b plumbers? (b) what is the hourly rate that j&b charges? (c) calculate the value of $c(0)$ and explain its meaning.

Explanation:

Step1: Identify service - charge in linear function

The linear function is $C(h)=50 + 20h$. In a linear function of the form $y = mx + b$, the initial value (y - intercept) is $b$. Here, the service - charge is the constant term. So the service - charge is $\$50$.

Step2: Identify hourly rate in linear function

In the linear function $C(h)=50 + 20h$, the coefficient of $h$ represents the rate of change. In the context of the problem, it is the hourly rate. So the hourly rate is $\$20$ per hour.

Step3: Calculate $C(0)$ and explain

Substitute $h = 0$ into $C(h)=50+20h$. We get $C(0)=50 + 20\times0=50$. This means that if the plumber does not work any hours (just comes to the house), the customer still has to pay the service - charge of $\$50$.

Answer:

(a) $\$50$
(b) $\$20$ per hour
(c) $C(0) = 50$. It means the customer pays the service - charge of $\$50$ when the plumber does not work any hours (just arrives at the house).