Question
Write a symbolic representation for a linear function that computes the following. The long distance phone bill in dollars for calling \( t \) minutes at 30 cents per minute and a fixed fee of \( \$ 4.95 \).
Ask by Stephens Wilson. in the United States
Mar 13,2025
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Answer
The linear function for the phone bill is \( B(t) = 0.30t + 4.95 \).
Solution
To represent the long distance phone bill as a linear function, we can define the function \( B(t) \) where:
- \( B(t) \) is the total bill in dollars.
- \( t \) is the number of minutes called.
- The cost per minute is \( 0.30 \) dollars (30 cents).
- There is a fixed fee of \( 4.95 \) dollars.
The total bill can be calculated using the formula:
\[
B(t) = 0.30t + 4.95
\]
Here, \( 0.30t \) represents the variable cost based on the number of minutes called, and \( 4.95 \) is the fixed fee.
Thus, the symbolic representation of the linear function is:
\[
B(t) = 0.30t + 4.95
\]
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The long-distance phone bill can be represented by the linear function \( B(t) = 0.30t + 4.95 \), where \( B(t) \) is the total bill in dollars, \( t \) is the number of minutes called, and 0.30 represents the cost per minute. This means for every minute you talk, you add 30 cents to your total, plus a basic charge of $4.95. Understanding how this function works in practical scenarios can be useful. For instance, if you planned to chat for 20 minutes, you would simply plug in \( t = 20 \) into the equation: \( B(20) = 0.30(20) + 4.95 = 6.95 \). So, your phone bill would be $6.95 for that call. Quite handy for budgeting those long-distance chats!
