Question

question 2 points 3

a company rents bicycles. they charge a flat fee of $10 plus $4 per hour for the first 5 hours. after 5 hours, the hourly charge drops to $3 per hour.
which piecewise function c(h) correctly models the total cost c for renting a bike for h hours?

\\( c(h) = \

$$\begin{cases} 10 + 4h & h \\le 5 \\\\ 10 + 20 + 3(h - 5) & h > 5 \\end{cases}$$

\\)

\\( c(h) = \

$$\begin{cases} 10 + 4h & h \\le 5 \\\\ 10 + 3h & h > 5 \\end{cases}$$

\\)

Explanation:

Model cost for first interval

Using the Cost Functions knowledge point

$$ C(h) = 10 + 4h \quad \text{for } h \le 5 $$

Calculate cost at boundary

Using the Cost Functions knowledge point

$$ C(5) = 10 + 4(5) = 10 + 20 = 30 $$

Model cost for second interval

For \(h > 5\), the cost is the total accumulated cost for the first 5 hours plus the new hourly rate of \$3 for any additional hours beyond 5:

$$ C(h) = C(5) + 3(h - 5) = 10 + 20 + 3(h - 5) $$

Combine into piecewise function

Combining both intervals yields:

$$ C(h) =
LATEXBLOCK0
$$

Answer:

• **(A) \(C(h) =

$$\begin{cases} 10 + 4h & h \le 5 \\ 10 + 20 + 3(h - 5) & h > 5 \end{cases}$$

\) (Correct answer)**

• (B) \(C(h) =

$$\begin{cases} 10 + 4h & h \le 5 \\ 10 + 3h & h > 5 \end{cases}$$

\)