Questions: Write a linear cost function for the situation. Identify all variables used. A parking garage charges 8 dollars plus 25 cents per half-hour. Identify all variables used. Choose the correct answer below. A. C(x) represents the cost for using the parking garage for x half-hours. B. C(x) represents the number of hours the parking garage was used after paying x dollars. C. C(x) represents the cost for parking x cars in the parking garage. D. C(x) represents the number of half-hours the parking garage was used after paying x dollars.

Write a linear cost function for the situation. Identify all variables used.
A parking garage charges 8 dollars plus 25 cents per half-hour.

Identify all variables used. Choose the correct answer below.
A. C(x) represents the cost for using the parking garage for x half-hours.
B. C(x) represents the number of hours the parking garage was used after paying x dollars.
C. C(x) represents the cost for parking x cars in the parking garage.
D. C(x) represents the number of half-hours the parking garage was used after paying x dollars.

Transcript text: Write a linear cost function for the situation. Identify all variables used. A parking garage charges 8 dollars plus 25 cents per half-hour. Identify all variables used. Choose the correct answer below. A. $C(x)$ represents the cost for using the parking garage for $x$ half-hours. B. $C(x)$ represents the number of hours the parking garage was used after paying $x$ dollars. C. $C(x)$ represents the cost for parking $x$ cars in the parking garage. D. $\mathrm{C}(\mathrm{x})$ represents the number of half-hours the parking garage was used after paying x dollars.

Solution

Solution Steps

Step 1: Identify the variables

The problem involves a parking garage that charges a fixed fee plus a variable fee based on the duration of parking. The fixed fee is \$8, and the variable fee is \$0.25 per half-hour. The variable $ x $ represents the number of half-hours the parking garage is used.

Step 2: Define the cost function

The cost function $ C(x) $ represents the total cost for using the parking garage for $ x $ half-hours. It is calculated as the sum of the fixed fee and the variable fee multiplied by the number of half-hours: \[ C(x) = 8 + 0.25x \]

Step 3: Choose the correct variable interpretation

From the given options:

A. $ C(x) $ represents the cost for using the parking garage for $ x $ half-hours.
B. $ C(x) $ represents the number of hours the parking garage was used after paying $ x $ dollars.
C. $ C(x) $ represents the cost for parking $ x $ cars in the parking garage.
D. $ C(x) $ represents the number of half-hours the parking garage was used after paying $ x $ dollars.

The correct interpretation is A, as $ C(x) $ represents the cost for using the parking garage for $ x $ half-hours.