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.
Linear model: $C = 1.50h + b$

Step2: Substitute known values

Plug $C=15$, $h=6$ into model:
$15 = 1.50(6) + b$

Step3: Calculate rental fee (initial value)

First compute $1.50(6)=9$, then solve for $b$:
$b = 15 - 9 = 6$

Step4: Identify rate of change

The coefficient of $h$ is the hourly rate.

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.