A parking garage charges the rate in the table below. What is the rate of change? Don’t forget your units.
no. hours: 1 3 5
cost of parking: $10 $14 $16
To find the rate of change, we need to calculate the change in cost of parking per hour:
Change in cost = (new cost - old cost) / (new number of hours - old number of hours)
For the first pair of values (1 hour and $10) and the second pair of values (3 hours and $14):
Change in cost = ($14 - $10) / (3 hours - 1 hour)
= $4 / 2 hours
= $2/hour
For the second pair of values (3 hours and $14) and the third pair of values (5 hours and $16):
Change in cost = ($16 - $14) / (5 hours - 3 hours)
= $2 / 2 hours
= $1/hour
Therefore, the rate of change in cost of parking is $2/hour for the first pair of values and $1/hour for the second pair of values.
now use another point for x2 and y2
(3,14)
(5,16)
To find the rate of change using the new points (3,14) and (5,16), we can follow the same steps as before:
Change in cost = (new cost - old cost) / (new number of hours - old number of hours)
For the first pair of values (1 hour and $10) and the new pair of values (3 hours and $14):
Change in cost = ($14 - $10) / (3 hours - 1 hour)
= $4 / 2 hours
= $2/hour
For the new pair of values (3 hours and $14) and (5 hours and $16):
Change in cost = ($16 - $14) / (5 hours - 3 hours)
= $2 / 2 hours
= $1/hour
The rate of change in cost of parking is still $2/hour for the first pair of values and $1/hour for the new pair of values.
To find the rate of change, we need to determine how the cost of parking changes as the number of hours increases.
Let's calculate the rate of change for each increase in the number of hours:
For 1 hour to 3 hours:
Change in cost = $14 - $10 = $4
Change in hours = 3 - 1 = 2
Rate of change = Change in cost / Change in hours
Rate of change = $4 / 2 hours = $2 per hour
For 3 hours to 5 hours:
Change in cost = $16 - $14 = $2
Change in hours = 5 - 3 = 2
Rate of change = Change in cost / Change in hours
Rate of change = $2 / 2 hours = $1 per hour
So, the rate of change for this parking garage is $2 per hour for the first two hours and $1 per hour for the next two hours.