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

Kathryn Kingham

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

What is the rate of change of the data given in the table below?

Rate of change is a rate that describes how one quantity changes in relation to another quantity. And we wanna know what is the rate of change that’s represented in this table. Our relationship in our two quantities would be the remaining gallons of gas related to the miles driven in your car. A simplified way to say that is we wanna relate the remaining gallons to the miles driven. So our rate of change will be comparing how do the gallons change as the miles driven change.

To solve that, we need to look at our table. In the first row, we’ll looking at the remaining gallons of gas. Between the first two columns are gases gone from nineteen gallons to fourteen gallons, a decrease of five gallons. At the same time, the miles we’ve driven has gone from zero to one hundred. We’ve added one hundred miles at the same time that we’ve used five gallons of gas.

We’ll look at the next two columns to see if the same pattern continues. We move from fourteen gallons of gas remaining to nine gallons of gas remaining, which is another decrease in five gallons. We’ve also moved from one hundred miles driven to two hundred miles driven, another increase of one hundred miles.

Looking at the last two columns, we’ve gone from nine gallons to four gallons. We’ve used five gallons in between this time period. And in that same amount of time, we’ve driven from two hundred miles up to three hundred miles, an increase of one hundred miles.

Our rate here is decreasing five gallons for every one hundred miles that we drive. Based on the table, we can say that there is a decrease in five gallons of gas for every one hundred miles we drive. And that’s what we would write as the rate of change based on the data in the table.