A rate of change is a ratio of the amount of change in the dependent variable to the amount of change in the independent variable.
Example 1 :
Eve keeps a record of the number of lawns she has mowed and the money she has earned. Tell whether the rates of change are constant or variable.
Solution :
Step 1 :
Identify the independent and dependent variables.
Independent : Number of lawns
Dependent : Amount earned
Step 2 :
Find the rates of change.
Day 1 to Day 2 :
Change in $/Change in lawns = (45 - 15)/(3 - 1)
Change in $/Change in lawns = 30/2
Change in $/Change in lawns = 15
Day 2 to Day 3 :
Change in $/Change in lawns = (90 - 45)/(6 - 3)
Change in $/Change in lawns = 45/3
Change in $/Change in lawns = 15
Day 3 to Day 4 :
Change in $/Change in lawns = (120 - 90)/(8 - 6)
Change in $/Change in lawns = 30/2
Change in $/Change in lawns = 15
The rates of change are constant : $15 per lawn.
Example 2 :
The table shows the approximate height of a football after it is kicked. Tell whether the rates of change are constant or variable.
Solution :
Step 1 :
Identify the independent and dependent variables.
Independent : Time
Dependent : Height
Step 2 :
Find the rates of change.
0 seconds to 0.5 seconds :
Change in height/Change in time = (18 - 0)/(0.5 - 0)
Change in height/Change in time = 18/0.5
Change in height/Change in time = 36
0.5 seconds to 1.5 seconds :
Change in height/Change in time = (31 - 18)/(1.5 - 0.5)
Change in height/Change in time = 13/1
Change in height/Change in time = 13
1.5 seconds to 2 seconds :
Change in height/Change in time = (26 - 31)/(2 - 1.5)
Change in height/Change in time = -5/0.5
Change in height/Change in time = -10
The rate of change are variable.
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