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Video: Identifying the Appropriate Expression for Interpreting the Rate of Change

Bethani Gasparine

Which of the following interprets the rate of change of the data in the table? [A] a decrease of 5 gallons per 100 miles [B] a decrease of 5 gallons per 50 miles [C] a decrease of 19 gallons per 100 miles [D] a decrease of 19 gallons per 50 miles [E] a decrease of 5 gallons per 100 miles

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Video Transcript

Interpret the rate of change of the data in the table.

Here we have the remaining gas, which is in gallons, and miles driven, which is in miles. So the gallons go from 19 to 14 to nine to four; the miles driven go from zero miles to 100 to 200 to 300.

A rate of change is a rate that describes how one quantity changes in relation to another quantity. So here we’re gonna be looking at how gallons change in relation to how the miles change. So let’s look at how each number is changing.

To go from 19 gallons to 14 gallons, we decrease by five gallons. To go from 14 gallons to nine gallons, we again decreased by five gallons. And finally to go from nine gallons to four gallons, we also decrease by five gallons.

Now let’s take a look at the miles. To go from zero miles to 100 miles, we increase by 100 miles. To go from 100 miles to 200 miles, we increase by 100 miles. And from 200 to 300 miles, we also increase by 100 miles. We can actually look at the size of fractions as well.

We’re comparing the changing gallons to the change in miles. To go from 19 gallons to 14 gallons, you would have to decrease by five gallons. And to go from zero miles to 100 miles, you will have to increase by 100 miles. Therefore, the interpretation from this table would be a decrease of five gallons per 100 miles.