Calculate, estimate, and interpret average rate of change over an interval.
Interpret average rate of change with units
Problem
Distance \(d(t)\), in miles, has average rate of change \(60~\text{miles}~\text{per}~\text{hour}\) from \(t~=~2\) to \(t~=~5~\text{hours}\). Calculate the input and output changes, state the units, and interpret the average rate and total change in context.
Big Picture
What this problem is really about
An average rate and a total change describe related but different quantities. We’ll find the interval’s elapsed time, read the rate’s sign and output-per-input units, and multiply rate by elapsed time to recover the total output change. The final interpretation should say both what changes across the whole interval and how much it changes on average per hour.
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