Final answer:
The rate of change in this situation is $3 per hour. This means that for every additional hour of skating, the total cost increases by $3.
Step-by-step explanation:
The rate of change represents how one variable changes with respect to another variable. In this case, the roller skating rink charges a skate rental fee and an hourly rate to skate. To find the rate of change, we can use the given information about the total cost to skate for different durations.
Let's use the values of total cost and duration to find the rate of change.
- For 2 hours: total cost = $9.50
- For 5 hours: total cost = $18.50
To find the rate of change, we can calculate the difference in the total cost and duration. Then divide the change in cost by the change in duration.
Rate of change = (change in total cost) / (change in duration)
Rate of change = ($18.50 - $9.50) / (5 hours - 2 hours)
Rate of change = $9 / 3 hours
Therefore, the rate of change is $3 per hour. This means that for every additional hour of skating, the total cost increases by $3.