During a study, the temperature, in   degrees   Celsius   ° C , of the air in a chamber

Question

During a study, the temperature, in &#160; degrees &#160; Celsius &#160; &#176; C , of the air in a chamber was recorded to the nearest integer at certain times. The sterplot shows the recorded temperature y , in &#160; &#176; C , of the air in the chamber x minutes after the start of the study. 1 2 3 4 5 6 7 8 x 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 y O Time (minutes) Temperature ( The sterplot has 7 data points. The data points are in a linear pattern trending up from left to right. The data points have the following coordinates: (1 comma 4) (2 comma 6) (3 comma 12) (4 comma 10) (5 comma 14) (6 comma 16) (7 comma 24) What was the average rate of change, in &#160; &#176; C per minute, of the recorded temperature of the air in the chamber from x = 5 to x = 7 ?

Accepted Answer

The correct answer is 5 . For the graph shown, x represents time, in minutes, and y represents temperature, in degrees Celsius &deg; C . Therefore, the average rate of change, in &deg; C per minute, of the recorded temperature of the air in the chamber between two x -values is the difference in the corresponding y -values divided by the difference in the x -values. The graph shows that at x = 5 , the corresponding y -value is 14 . The graph also shows that at x = 7 , the corresponding y -value is 24 . It follows that the average rate of change, in &deg; C per minute, from x = 5 to x = 7 is 24 - 14 7 - 5 , which is equivalent to 10 2 , or 5 .

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