Question

Sophia is going to use a computer at an internet cafe. The cafe charges an

initial fee to use the computer and then an additional price per minute of
usage. Let C represent the total cost of using a computer for t minutes at
the internet cafe. A graph of C is shown below. Write an equation for C
then state the slope of the graph and determine its interpretation in the
context of the problem.
Total Cost to Use Computer
1
C=
5 6 7
Number of Minutes
Answer Attempt 5 out of 10
The slope of the function is
which represents
B

Answer 1

The equation
`\(C(t) = (1)/(5)t + 1\)` represents the total cost \(C\) of using a computer for
`\(t\)` minutes at the internet cafe. The slope
`\((1)/(5)\)` signifies a cost increase of
`\( (1)/(5) \)` dollars per minute.

The equation for the total cost of using a computer at the internet cafe,
`\(C(t)\)`, is expressed as
`\(C(t) = (1)/(5)t + 1\)`, where
`\(t\)` is the number of minutes used. This equation reflects the cafe's pricing structure, with the term
`\((1)/(5)t\)` representing the cost per minute of computer usage and the constant term 1 representing the initial fee.

The slope of the function is
`\((1)/(5)\).` In the context of the problem, this slope signifies the rate of change in cost concerning time, specifically the cost per minute. For every additional minute of computer usage, the cost increases by
`\((1)/(5)\)` units. Therefore, the cafe charges
`\( (1)/(5) \)` dollars per minute for utilizing their computer services.

The graph visually illustrates this linear relationship, showing a steady increase in the total cost as the number of minutes used (the independent variable) increases. The initial fee contributes to the y-intercept, while the slope captures the incremental cost per minute.

Understanding the equation and slope provides customers insights into the cafe's pricing model, aiding in budgeting decisions for computer usage. It allows individuals to predict costs based on the time they plan to spend at the internet cafe, enhancing transparency in pricing for both the cafe and its customers.