Solve the problem. -A paddle boat rental company rents paddle boats by the hour. They charge $7.00 per hour for the first 3 rental hours and $5.00 per hour for each additional hour. Write a piecewise function to represent the cost of renting a Paddle boat as a function of hours it is rented. A) $f ( x ) = \left\{ \begin{array} { l l } 7 \llbracket x \rrbracket & \text { if } 0 3 \end{array} \right.$ B) $f ( x ) = \left\{ \begin{array} { l l } 7 \llbracket x \rrbracket & \text { if } 0 3 \end{array} \right.$ C) $f ( x ) = \left\{ \begin{array} { l l } 7 \llbracket x \rrbracket & \text { if } 0 3 \end{array} \right.$ D) $f ( x ) = \left\{ \begin{array} { l l } 7 \llbracket x \rrbracket & \text { if } 0 3 \end{array} \right.$

Question

Solve the problem. -A paddle boat rental company rents paddle boats by the hour. They charge $7.00 per hour for the first 3 rental hours and $5.00 per hour for each additional hour. Write a piecewise function to represent the cost of renting a Paddle boat as a function of hours it is rented. A) $f ( x ) = \left\{ \begin{array} { l l } 7 \llbracket x \rrbracket & \text { if } 0 < x \leq 3 \ 21 \llbracket x \rrbracket + 5 \llbracket x - 3 \rrbracket & \text { if } x > 3 \end{array} \right.$ B) $f ( x ) = \left\{ \begin{array} { l l } 7 \llbracket x \rrbracket & \text { if } 0 < x \leq 3 \ 7 \llbracket x \rrbracket + 5 \llbracket x - 3 \rrbracket & \text { if } x > 3 \end{array} \right.$ C) $f ( x ) = \left\{ \begin{array} { l l } 7 \llbracket x \rrbracket & \text { if } 0 < x \leq 3 \ 21 + 5 \llbracket x - 3 \rrbracket & \text { if } x > 3 \end{array} \right.$ D) $f ( x ) = \left\{ \begin{array} { l l } 7 \llbracket x \rrbracket & \text { if } 0 < x \leq 3 \ 5 \llbracket x - 3 \rrbracket & \text { if } x > 3 \end{array} \right.$

Quizplus · Accepted Answer

The correct piecewise function must account for the initial charge for the first 3 hours ($7 per hour) and then add the additional charge for hours beyond 3 at $5 per hour. For the first 3 hours, the cost is $7 times the number of hours. For hours beyond 3, the total cost is the initial $21 (3 hours at $7 each) plus $5 for each hour beyond 3. This is correctly represented in option C.

Solve the Problem B) C) D)