Question
The receptionist at the ABC Moving and Storage calculated the total amount of money owed for an x mile move according to the linear function below.
f(x) = 1,965 + 0.32(x - 660)
(where x > 660 miles)
What can be concluded about how much the customer is charged?
A.
The customer is charged $1,965 and a 32% surcharge for every mile over 660 miles.
B.
The customer is charged $1,965 plus $0.32 that doubles per mile over 660 miles.
C.
The customer is charged $1,965 times a discount of $0.32 for mileage under 660 miles.
D.
The customer is charged a flat rate of $1,965 plus $0.32 a mile for every mile over 660 miles.
f(x) = 1,965 + 0.32(x - 660)
(where x > 660 miles)
What can be concluded about how much the customer is charged?
A.
The customer is charged $1,965 and a 32% surcharge for every mile over 660 miles.
B.
The customer is charged $1,965 plus $0.32 that doubles per mile over 660 miles.
C.
The customer is charged $1,965 times a discount of $0.32 for mileage under 660 miles.
D.
The customer is charged a flat rate of $1,965 plus $0.32 a mile for every mile over 660 miles.
Answers
GPT-4o mini
To analyze the function \( f(x) = 1,965 + 0.32(x - 660) \), we can break it down as follows:
1. The term \( 1,965 \) represents a flat base fee for the move.
2. The term \( 0.32(x - 660) \) indicates an additional charge that is incurred for each mile over 660 miles. Specifically, \( x - 660 \) calculates the number of miles over 660, and then this number is multiplied by $0.32 to determine the additional charge.
Now, let's look at the provided options:
A. The customer is charged $1,965 and a 32% surcharge for every mile over 660 miles.
- This is incorrect because the additional charge is $0.32 per mile, not a 32% surcharge.
B. The customer is charged $1,965 plus $0.32 that doubles per mile over 660 miles.
- This is incorrect because the additional charge of $0.32 does not double; it remains constant at $0.32 per mile.
C. The customer is charged $1,965 times a discount of $0.32 for mileage under 660 miles.
- This is incorrect because the function does not imply a discount for mileage under 660 miles; the charge starts only when the mileage exceeds 660.
D. The customer is charged a flat rate of $1,965 plus $0.32 a mile for every mile over 660 miles.
- This is correct. The base fee is $1,965, and there is an additional charge of $0.32 for each mile that exceeds 660 miles.
Thus, the correct conclusion is:
**D. The customer is charged a flat rate of $1,965 plus $0.32 a mile for every mile over 660 miles.**
1. The term \( 1,965 \) represents a flat base fee for the move.
2. The term \( 0.32(x - 660) \) indicates an additional charge that is incurred for each mile over 660 miles. Specifically, \( x - 660 \) calculates the number of miles over 660, and then this number is multiplied by $0.32 to determine the additional charge.
Now, let's look at the provided options:
A. The customer is charged $1,965 and a 32% surcharge for every mile over 660 miles.
- This is incorrect because the additional charge is $0.32 per mile, not a 32% surcharge.
B. The customer is charged $1,965 plus $0.32 that doubles per mile over 660 miles.
- This is incorrect because the additional charge of $0.32 does not double; it remains constant at $0.32 per mile.
C. The customer is charged $1,965 times a discount of $0.32 for mileage under 660 miles.
- This is incorrect because the function does not imply a discount for mileage under 660 miles; the charge starts only when the mileage exceeds 660.
D. The customer is charged a flat rate of $1,965 plus $0.32 a mile for every mile over 660 miles.
- This is correct. The base fee is $1,965, and there is an additional charge of $0.32 for each mile that exceeds 660 miles.
Thus, the correct conclusion is:
**D. The customer is charged a flat rate of $1,965 plus $0.32 a mile for every mile over 660 miles.**