Question
An electrician charges a set fee for every house call and then charges an hourly rate depending on how long the job takes. Let CC represent the total cost of the visit when the electrician spends tt hours at the house working. A graph of CC is shown below. Write an equation for CC then state the yy-intercept of the graph and determine its interpretation in the context of the problem.
0
Number of Hours Working
Total Cost for Electrician Services
t
C
0
Number of Hours Working
Total Cost for Electrician Services
Answer
Attempt 1 out of 2
C, equalsC=
The yy-intercept of the function is
which represents
0
Number of Hours Working
Total Cost for Electrician Services
t
C
0
Number of Hours Working
Total Cost for Electrician Services
Answer
Attempt 1 out of 2
C, equalsC=
The yy-intercept of the function is
which represents
Answers
Answered by
GPT-4o mini
To derive the equation for \( C \), we can use the information from the graph. Typically, the cost function for a service like this can be expressed as:
\[
C = C_0 + r \cdot t
\]
where:
- \( C_0 \) is the fixed fee (the y-intercept).
- \( r \) is the hourly rate (the slope of the line).
- \( t \) is the number of hours worked.
To find the y-intercept \( C_0 \), we look at the value of \( C \) when \( t = 0 \). This value represents the fixed fee charged by the electrician for just making the house call, regardless of how long they actually work.
For example, if on the graph the total cost \( C \) when \( t = 0 \) is shown at a specific value (let's say $50), then:
\[
C_0 = 50
\]
The equation would look like this (assuming an hourly rate of $30 for instance):
\[
C = 50 + 30t
\]
Thus,
### Answer
The equation for \( C \) is \( C = C_0 + rt \).
If we take \( C_0 = 50 \) and \( r = 30 \) as an example:
\[
C = 50 + 30t
\]
The y-intercept of the function is at \( C_0 = 50 \), which represents the fixed cost that the electrician charges just for arriving at a house, regardless of the time spent on the job.
\[
C = C_0 + r \cdot t
\]
where:
- \( C_0 \) is the fixed fee (the y-intercept).
- \( r \) is the hourly rate (the slope of the line).
- \( t \) is the number of hours worked.
To find the y-intercept \( C_0 \), we look at the value of \( C \) when \( t = 0 \). This value represents the fixed fee charged by the electrician for just making the house call, regardless of how long they actually work.
For example, if on the graph the total cost \( C \) when \( t = 0 \) is shown at a specific value (let's say $50), then:
\[
C_0 = 50
\]
The equation would look like this (assuming an hourly rate of $30 for instance):
\[
C = 50 + 30t
\]
Thus,
### Answer
The equation for \( C \) is \( C = C_0 + rt \).
If we take \( C_0 = 50 \) and \( r = 30 \) as an example:
\[
C = 50 + 30t
\]
The y-intercept of the function is at \( C_0 = 50 \), which represents the fixed cost that the electrician charges just for arriving at a house, regardless of the time spent on the job.