Math Problem Statement

A taxicab ride costs $3.50 plus $2.50 per mile. Let m be the distance (in miles) from the airport to a hotel. Find and graph the function c(m) that represents the cost of taking a taxi from the airport to the hotel. Also, determine how much it costs if the hotel is 8 miles from the airport.

Solution

Here's the graph of the function c(m)=3.5+2.5mc(m) = 3.5 + 2.5m representing the cost of a taxicab ride as a function of distance from the airport. The red point on the graph at (8,23.5)(8, 23.5) indicates the cost for a ride to a hotel 8 miles away from the airport, which is $23.50.

Would you like more details on this topic or have any other questions?

Here are some related questions you might consider:

  1. How would the cost function change if the per-mile rate increased?
  2. What would the intercept represent in a real-life scenario?
  3. How would you calculate the cost for a round trip?
  4. Can you find the distance if the total cost is given, say $50?
  5. How do variations in flat rates affect the overall cost function?

Tip: When analyzing a linear cost function like this, consider the slope and intercept for insights into variable and fixed costs respectively.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Algebra

Formulas

c(m) = 3.50 + 2.50m

Theorems

Slope-Intercept Form of a Linear Equation

Suitable Grade Level

Grades 7-9