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Two-variable data: Models and scatterplots SAT question

Math · Problem-Solving and Data Analysis · Easy · Answer it here, explanation included.

The figure presents a scatterplot titled “Temperature of a Cup of Coffee during an Experiment.” The horizontal axis is labeled “Time since cup was removed from heat source, in minutes,” and the numbers 0 through 140, in increments of 20, are indicated. The vertical axis is labeled “Temperature, in degrees Fahrenheit,” and the numbers 0 through 220, in increments of 20, are indicated. There are 15 data points in the scatterplot. The data points begin with point 0 comma 195, and trend downward and to the right, rapidly at first, then more and more slowly, finally leveling off. The last data point is 140 comma 76. The 15 data points are as follows. The second coordinate of each point is approximate. Point 1, 0 comma 195. Point 2, 10 comma 153. Point 3, 20 comma 136. Point 4, 30 comma 122. Point 5, 40 comma 109. Point 6, 50 comma 100. Point 7, 60 comma 92. Point 8, 70 comma 84. Point 9, 80 comma 82. Point 10, 90 comma 80. Point 11, 100 comma 79. Point 12, 110 comma 77. Point 13, 120 comma 77. Point 14, 130 comma 76. Point 15, 140 comma 76.

In an experiment, a heated cup of coffee is removed from a heat source, and the cup of coffee is then left in a room that is kept at a constant temperature. The graph above shows the temperature, in degrees Fahrenheit (°F), of the coffee immediately after being removed from the heat source and at 10-minute intervals thereafter. During which of the following 10-minute intervals does the temperature of the coffee decrease at the greatest average rate?

ExplanationShow

Choice A is correct. The average rate of change in temperature of the coffee in degrees Fahrenheit per minute is calculated by dividing the difference between two recorded temperatures by the number of minutes in the corresponding interval of time. Since the time intervals given are all 10 minutes, the average rate of change is greatest for the points with the greatest difference in temperature. Of the choices, the greatest difference in temperature occurs between 0 and 10 minutes.

Choices B, C, and D are incorrect and may result from misinterpreting the average rate of change from the graph.

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