Science · Original worked example
Calculate a rate from changes in the data
Find an average rate from a science data table, distinguish a final reading from a change, and keep the units straight in an original practice question.
Before you begin
Useful foundation: Subtract measurements with matching units and divide one change by another.
Your goal: Calculate an average rate over a specified interval without assuming the rate was constant throughout.
Average rate of change is the change in the measured quantity divided by the elapsed time. On a quantity-versus-time graph, this is the slope between the two endpoints. Include both units and preserve the sign when the quantity decreases.
Work through an example
A tank is filled while a sensor records its volume. Use the original illustrative measurements below to find the average filling rate from 2 to 6 minutes.
| Time (min) | Volume (L) |
|---|---|
| 0 | 12 |
| 2 | 20 |
| 6 | 44 |
- Use the specified endpoints: the volume is 20 L at 2 min and 44 L at 6 min.
- Find the volume change: 44 − 20 = 24 L. The final reading of 44 L is not the amount added during this interval.
- Find the elapsed time: 6 − 2 = 4 min. Divide: 24 L ÷ 4 min = 6 L/min.
- This is an average over the interval. The endpoint measurements alone do not establish a constant rate at every moment between them.
Try a question yourself
In a separate original experiment, a gas collector contains 9 mL at 1 minute and 33 mL at 5 minutes.
Choose an answer, then check your reasoning. This public practice is not saved.
Read all answer explanations
24 mL/min: 24 mL is the change in volume. Divide that change by the 4-minute interval to get a rate.
6 mL/min — correct answer: Yes. (33 − 9) mL ÷ (5 − 1) min = 24 ÷ 4 = 6 mL/min.
6.6 mL/min: 33 ÷ 5 uses the final reading and final clock time. The requested interval starts at 1 minute with 9 mL already present.
8.25 mL/min: 33 ÷ 4 uses the correct time interval but fails to subtract the initial 9 mL. Use the change in both quantities.
What to do next
Compare rates over two different intervals. If you see a downward trend, keep the negative sign when finding a signed rate of change; use a positive magnitude only when asked for the amount of decrease.
Revisit the idea in a week using a different question. Repeating this example can help you understand it, but remembering its answer is not evidence of learning a new problem.
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