Question
Unit 7 Sample Work Retake
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Question
The function C(m)=2.5m+5 represents the cost to ride a certain amount of miles, m, in a taxi. The cost also includes a one-time charge to get in the taxi.
a) What is the cost per mile?
b) How much is the one-time charge to get in the taxi?
c) How much will the total cost be to ride 10 miles?
d) Does finding C(-5) make sense in the context of this function?
Unit 7 Sample Work Retake
3 of 153 of 15 Items
Question
The function represents the cost to ride a certain amount of miles, m, in a taxi. The cost also includes a one-time charge to get in the taxi.
a) What is the cost per mile?
b) How much is the one-time charge to get in the taxi?
c) How much will the total cost be to ride 10 miles?
d) Does finding make sense in the context of this function?
Answers
Answered by
GPT-4o mini
Let's analyze the function \( C(m) = 2.5m + 5 \) step by step.
### a) What is the cost per mile?
The cost per mile is represented by the coefficient of \( m \) in the function. Here, \( C(m) = 2.5m + 5 \), so the cost per mile is:
\[
\text{Cost per mile} = 2.5
\]
### b) How much is the one-time charge to get in the taxi?
The one-time charge to get in the taxi is represented by the constant term in the function. In this case, the constant term is \( 5 \). Therefore, the one-time charge is:
\[
\text{One-time charge} = 5
\]
### c) How much will the total cost be to ride 10 miles?
To find the total cost to ride 10 miles, we substitute \( m = 10 \) into the function:
\[
C(10) = 2.5(10) + 5
\]
\[
C(10) = 25 + 5
\]
\[
C(10) = 30
\]
Thus, the total cost to ride 10 miles is:
\[
\text{Total cost} = 30
\]
### d) Does finding \( C(-5) \) make sense in the context of this function?
Finding \( C(-5) \) would imply that you want to find the cost for riding a negative distance of -5 miles. In practical terms, negative distance does not make sense in the context of riding in a taxi. Therefore, finding \( C(-5) \) does not make sense in this context.
**Summary:**
a) Cost per mile: 2.5
b) One-time charge: 5
c) Total cost for 10 miles: 30
d) Finding \( C(-5) \) does not make sense.
### a) What is the cost per mile?
The cost per mile is represented by the coefficient of \( m \) in the function. Here, \( C(m) = 2.5m + 5 \), so the cost per mile is:
\[
\text{Cost per mile} = 2.5
\]
### b) How much is the one-time charge to get in the taxi?
The one-time charge to get in the taxi is represented by the constant term in the function. In this case, the constant term is \( 5 \). Therefore, the one-time charge is:
\[
\text{One-time charge} = 5
\]
### c) How much will the total cost be to ride 10 miles?
To find the total cost to ride 10 miles, we substitute \( m = 10 \) into the function:
\[
C(10) = 2.5(10) + 5
\]
\[
C(10) = 25 + 5
\]
\[
C(10) = 30
\]
Thus, the total cost to ride 10 miles is:
\[
\text{Total cost} = 30
\]
### d) Does finding \( C(-5) \) make sense in the context of this function?
Finding \( C(-5) \) would imply that you want to find the cost for riding a negative distance of -5 miles. In practical terms, negative distance does not make sense in the context of riding in a taxi. Therefore, finding \( C(-5) \) does not make sense in this context.
**Summary:**
a) Cost per mile: 2.5
b) One-time charge: 5
c) Total cost for 10 miles: 30
d) Finding \( C(-5) \) does not make sense.
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