Question

1. a water park charges a rental fee plus $1.50 per hour to rent inflatable rafts. the total cost to rent a raft for 6 hours is $15. assume the relationship is linear. find and interpret the rate of change and the initial value. (example 2)

Explanation:

Step1: Define linear cost model

Let $C$ = total cost, $h$ = hours, $b$ = rental fee (initial value). The linear model is:
$$C = 1.50h + b$$

Step2: Plug in known values

We know $C=15$ when $h=6$:
$$15 = 1.50(6) + b$$

Step3: Calculate hourly cost total

Compute $1.50\times6$:
$$1.50(6) = 9$$

Step4: Solve for initial value $b$

Rearrange to isolate $b$:
$$b = 15 - 9 = 6$$

Answer:

• Rate of change: $\$1.50$ per hour, which is the additional cost to rent the raft for each extra hour.
• Initial value: $\$6$, which is the fixed rental fee charged regardless of how many hours the raft is rented.