Math Problem Statement

Write a symbolic representation for a linear function that computes the following. The long distance phone bill in dollars for calling t minutes at 4040 cents per minute and a fixed fee of ​$2.95

Solution

The long-distance phone bill can be represented as a linear function where the total cost depends on the number of minutes tt called.

Here's the symbolic representation:

C(t)=0.4040t+2.95C(t) = 0.4040t + 2.95

Where:

  • C(t)C(t) is the total phone bill in dollars,
  • tt is the number of minutes,
  • 0.40400.4040 is the cost per minute in dollars (converted from 40.40 cents), and
  • 2.952.95 is the fixed fee in dollars.

Would you like to explore more details or ask any questions?

Related Questions:

  1. How would the function change if the rate per minute was different?
  2. What is the cost for a 30-minute call?
  3. How can we determine the total cost for tt minutes without the fixed fee?
  4. How does this linear function graph look for various values of tt?
  5. How would the fixed fee affect the overall cost if it were higher?

Tip: Always double-check the unit conversion, especially when working with cents to dollars.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Algebra
Unit Conversion

Formulas

C(t) = 0.4040t + 2.95

Theorems

Linear Equation

Suitable Grade Level

Grades 7-9