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.

C = 6 + 1.5h.

$6 is the fixed fee that the park charges.

And $1.5 is the rate of charge per hour for rent of the raft.

Step-by-step explanation:

The water park charges a rental fee plus $1.5 per hour to rent inflatable rafts.

Let the total charge (C) has a linear relationship with the number of hours (h) spent in the park and it is C = a + bh ... (1)

Now, b is the rate of charge to rent inflatable rafts and b = $1.5 per hour.

So, C = a + 1.5h ... (2)

Now, given that the total cost to rent a raft for 6 hours is $15.

So, from equation (2) we get,

15 = a + 1.5 * 6

⇒ a = 6

Therefore, the equation (2) becomes C = 6 + 1.5h.

Here, $6 is the fixed fee that the park charges.

And $1.5 is the rate of charge per hour for rent of the raft. (Answer)