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Lesson 2: Constant Rate of Change Student Page A
Constant Rate of Change
Recall our definition of Constant Rate of Change: Two quantities are related by a constant rate of change if the changes in the quantities are proportional to one another.
- The height of water in a tank and the amount of time that has elapsed are given in the table. a. Demonstrate that the quantities are not proportional to one another.
b. Demonstrate that the quantities are related by a constant rate of change (that is, the changes in quantities are proportional).
Time Elapsed in min t
Height of water in tank in cm h
1.8 13.
2.5 15.
3.9 20.
7.4 33.
How to Determine the Constant Rate of Change In general, If two quantities are related by a constant rate of change of output with respect to input , we can determine the value of that rate by…
Lesson 2: Constant Rate of Change Student Page A
- Assume that the height of water in the tank instead increases at a constant rate of 3.5 cm per minute… a. How much will the height of water in the tank increase by i. in 2 minutes? ii. in 6 minutes? iii. In 7.8 minutes?
b. How much less was the height of water in the tank 3.1 minutes earlier (from any time/height measurement)?
c. If I know that the top of the tank is 18 cm above the current height of water, how much more time should I let the water run so that it is full?
d. Explain the meaning of the coordinate points (0.7, 6.45) and (10.3, 40.05) given in the table and graph.
e. Represent a change in time of 2 minutes from 0.7 minutes on the table and graph. Then, represent the associated change in height of water (found in part a) on both. f. Represent a change in time of 6 minutes from 0.7 minutes on the table and graph. Then, represent the associated change in height of water (found in part a) on both. g. Represent a change in time of –3.1 minutes from 10.3 minutes on the table and graph. Then, represent the associated change in height of water (found in part c) on both. h. Represent a change in height of 18 cm from 40.05 cm on the table and graph. Then, represent the associated change in time elapsed (found in part d) on both.
Time elapsed (in min)
Height of water (in cm)
Lesson 2: Constant Rate of Change Student Page A
- For each of the following tables, a. Explain whether or not the quantities are related by a constant rate of change (that is, whether the changes in the quantities are proportional).
b. For each table that is related by a constant rate of change, list the constant rate of change for that table.
a y m b –4 –42.8 –6 35.
–1.6 –26.72 –3.1 24.
3.6 9.12 2.6 1.
