1. **Problem Statement:** We need to sketch the cost of renting snowshoes for the first five hours, where the cost is $7 for the first hour or less, and $4 for each additional hour or part of an hour. 2. **Formula and Explanation:** The cost function $C(t)$ for time $t$ hours can be described as: $$ C(t) = 7 + 4 \times \lceil t - 1 \rceil \quad \text{for } t > 1 $$ where $\lceil x \rceil$ is the ceiling function, which rounds $x$ up to the nearest integer. - For $0 < t \leq 1$, cost is $7$. - For each additional hour or part thereof beyond the first hour, add $4$. 3. **Stepwise Cost Calculation:** - $0 < t \leq 1$: $C(t) = 7$ - $1 < t \leq 2$: $C(t) = 7 + 4 = 11$ - $2 < t \leq 3$: $C(t) = 7 + 8 = 15$ - $3 < t \leq 4$: $C(t) = 7 + 12 = 19$ - $4 < t \leq 5$: $C(t) = 7 + 16 = 23$ 4. **Graph Description:** The graph is a step function starting at $7$ for $t$ in $[0,1]$, then jumps to $11$ at $t=1$, stays constant until $t=2$, jumps to $15$ at $t=2$, and so on, increasing by $4$ at each integer hour after the first. 5. **Learner-friendly Explanation:** Think of the cost as a base fee of $7$ for the first hour. After that, every hour or part of an hour adds $4$. So if you rent for 1 hour and 1 minute, you pay for 2 hours total, which is $7 + 4 = 11$. The graph looks like steps because the cost jumps at each hour mark. **Final cost function:** $$ C(t) = \begin{cases} 7 & 0 < t \leq 1 \\ 7 + 4 \times \lceil t - 1 \rceil & t > 1 \end{cases} $$ **Answer:** The graph is a step function with values $7, 11, 15, 19, 23$ at hours $1, 2, 3, 4, 5$ respectively.