Get-Around Cab Company Charges $ 2.50 \$2.50 $2.50 Upon Entry And $ 2 \$2 $2 Per Mile. Write The Function That Represents The Cost C C C Of A Ride Of M M M Miles. C ( M ) = 2 M + 2.50 C(m) = 2m + 2.50 C ( M ) = 2 M + 2.50

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Introduction

In the world of mathematics, functions are used to describe the relationship between variables. In this article, we will explore the cost function of a taxi ride, specifically the Get-Around Cab Company. The company charges a fixed amount of $2.50\$2.50 upon entry and an additional $2\$2 per mile traveled. We will write a function that represents the cost CC of a ride of mm miles.

The Cost Function

The cost function of a taxi ride can be represented as C(m)=2m+2.50C(m) = 2m + 2.50, where CC is the cost of the ride and mm is the number of miles traveled. This function is a linear equation, where the cost is directly proportional to the number of miles traveled.

Breaking Down the Cost Function

Let's break down the cost function into its two components:

  • Fixed Cost: The fixed cost is the amount charged upon entry, which is $2.50\$2.50. This is a constant value that does not change regardless of the number of miles traveled.
  • Variable Cost: The variable cost is the amount charged per mile traveled, which is $2\$2. This value changes depending on the number of miles traveled.

Graphing the Cost Function

To visualize the cost function, we can graph it on a coordinate plane. The graph will be a straight line with a positive slope, since the cost increases as the number of miles traveled increases.

Example 1: Calculating the Cost of a 5-Mile Ride

Let's use the cost function to calculate the cost of a 5-mile ride.

C(m)=2m+2.50C(m) = 2m + 2.50 C(5)=2(5)+2.50C(5) = 2(5) + 2.50 C(5)=10+2.50C(5) = 10 + 2.50 C(5)=12.50C(5) = 12.50

The cost of a 5-mile ride is $12.50\$12.50.

Example 2: Calculating the Cost of a 10-Mile Ride

Let's use the cost function to calculate the cost of a 10-mile ride.

C(m)=2m+2.50C(m) = 2m + 2.50 C(10)=2(10)+2.50C(10) = 2(10) + 2.50 C(10)=20+2.50C(10) = 20 + 2.50 C(10)=22.50C(10) = 22.50

The cost of a 10-mile ride is $22.50\$22.50.

Conclusion

In this article, we have explored the cost function of a taxi ride, specifically the Get-Around Cab Company. The cost function is a linear equation that represents the relationship between the cost of a ride and the number of miles traveled. We have broken down the cost function into its two components, the fixed cost and the variable cost, and graphed the function on a coordinate plane. We have also used the cost function to calculate the cost of two example rides, a 5-mile ride and a 10-mile ride.

References

Q: What is the cost function of a taxi ride?

A: The cost function of a taxi ride is a linear equation that represents the relationship between the cost of a ride and the number of miles traveled. It is represented as C(m)=2m+2.50C(m) = 2m + 2.50, where CC is the cost of the ride and mm is the number of miles traveled.

Q: What are the two components of the cost function?

A: The two components of the cost function are the fixed cost and the variable cost. The fixed cost is the amount charged upon entry, which is $2.50\$2.50. The variable cost is the amount charged per mile traveled, which is $2\$2.

Q: How do I calculate the cost of a ride using the cost function?

A: To calculate the cost of a ride using the cost function, you need to plug in the number of miles traveled into the equation C(m)=2m+2.50C(m) = 2m + 2.50. For example, if you want to calculate the cost of a 5-mile ride, you would plug in m=5m = 5 into the equation.

Q: What is the cost of a 5-mile ride?

A: To calculate the cost of a 5-mile ride, you would plug in m=5m = 5 into the equation C(m)=2m+2.50C(m) = 2m + 2.50. This would give you C(5)=2(5)+2.50=10+2.50=12.50C(5) = 2(5) + 2.50 = 10 + 2.50 = 12.50. Therefore, the cost of a 5-mile ride is $12.50\$12.50.

Q: What is the cost of a 10-mile ride?

A: To calculate the cost of a 10-mile ride, you would plug in m=10m = 10 into the equation C(m)=2m+2.50C(m) = 2m + 2.50. This would give you C(10)=2(10)+2.50=20+2.50=22.50C(10) = 2(10) + 2.50 = 20 + 2.50 = 22.50. Therefore, the cost of a 10-mile ride is $22.50\$22.50.

Q: How does the cost function change if the fixed cost is increased?

A: If the fixed cost is increased, the cost function will change to C(m)=2m+cC(m) = 2m + c, where cc is the new fixed cost. For example, if the fixed cost is increased to $3.50\$3.50, the new cost function would be C(m)=2m+3.50C(m) = 2m + 3.50.

Q: How does the cost function change if the variable cost is increased?

A: If the variable cost is increased, the cost function will change to C(m)=2m+cC(m) = 2m + c, where cc is the new variable cost. For example, if the variable cost is increased to $3\$3 per mile, the new cost function would be C(m)=3m+2.50C(m) = 3m + 2.50.

Q: Can I use the cost function to calculate the cost of a ride that is not a multiple of 5 miles?

A: Yes, you can use the cost function to calculate the cost of a ride that is not a multiple of 5 miles. For example, if you want to calculate the cost of a 7-mile ride, you would plug in m=7m = 7 into the equation C(m)=2m+2.50C(m) = 2m + 2.50. This would give you C(7)=2(7)+2.50=14+2.50=16.50C(7) = 2(7) + 2.50 = 14 + 2.50 = 16.50. Therefore, the cost of a 7-mile ride is $16.50\$16.50.

Q: Can I use the cost function to calculate the cost of a ride that is not a multiple of 10 miles?

A: Yes, you can use the cost function to calculate the cost of a ride that is not a multiple of 10 miles. For example, if you want to calculate the cost of a 12-mile ride, you would plug in m=12m = 12 into the equation C(m)=2m+2.50C(m) = 2m + 2.50. This would give you C(12)=2(12)+2.50=24+2.50=26.50C(12) = 2(12) + 2.50 = 24 + 2.50 = 26.50. Therefore, the cost of a 12-mile ride is $26.50\$26.50.

Conclusion

In this article, we have answered some frequently asked questions about the cost function of a taxi ride. We have explained the cost function, its two components, and how to calculate the cost of a ride using the cost function. We have also provided examples of how to use the cost function to calculate the cost of rides that are not multiples of 5 or 10 miles.