Question

1. an internet service has a monthly access fee of $24.95 and a connection fee of $0.25 per hour. write a function that describes this situation for one month. if bonnie uses the internet for 7 hours and bill uses the internet for 4 hours, how much more does bonnie spend on the internet?

Explanation:

Part 1: Writing the function

Step1: Define variables

Let \( h \) be the number of hours of internet use in a month, and \( C(h) \) be the total cost for the month.

Step2: Determine fixed and variable costs

The monthly access fee is a fixed cost of \$24.95, and the connection fee is a variable cost of \$0.25 per hour. So the total cost function is the sum of the fixed cost and the variable cost.
The variable cost for \( h \) hours is \( 0.25h \) dollars.

Step3: Write the function

So the cost function \( C(h) = 24.95 + 0.25h \).

Part 2: Finding the difference in spending

Step1: Calculate Bonnie's cost

Bonnie uses the internet for 7 hours. Substitute \( h = 7 \) into the cost function \( C(h) \).
\( C(7)=24.95 + 0.25\times7 \)
\( C(7)=24.95 + 1.75 = 26.7 \) dollars.

Step2: Calculate Bill's cost

Bill uses the internet for 4 hours. Substitute \( h = 4 \) into the cost function \( C(h) \).
\( C(4)=24.95 + 0.25\times4 \)
\( C(4)=24.95 + 1 = 25.95 \) dollars.

Step3: Find the difference

Subtract Bill's cost from Bonnie's cost: \( 26.7 - 25.95 = 0.75 \) dollars.

Answer:

The cost function is \( C(h)=24.95 + 0.25h \), and Bonnie spends \$0.75 more than Bill.