Multiple Choice Rate of Change Question

Question

A chemist is experimenting with the properties of a chemical compound. He conducts an experiment in which he drops a sample of the chemical compound into a beaker and then applies even heat to the beaker over a period of 10 minutes. The Celsius temperature of the compound throughout the experiment, f(x), is shown in the following graph, where f(x)=0.3(x−5)3+34, and x is time in minutes.

Part A: During which time interval did the compound have the greatest average change in temperature?

Part B: The scientist’s experiment is contaminated when he accidentally lowers the heat being applied to the beaker. During which time interval did this accident most likely occur?

Choose one answer for Part A and one answer for Part B.

Options:

B: This most likely occurred from minute 4 to 6 because the average rate of temperature change in this interval is very small.

A: [0,2]

A: [0,6]

B: This most likely occurred from minute 8 to 10 because the average rate of temperature change in this interval is very great.

B: This most likely occurred from minute 0 to 2 because this is when the temperature of the compound is the lowest.

B: This most likely occurred from minute 6 to 10 because the average rate of temperature change in this interval is very small.

A: [6,8]

A: [8,10]

Answer 1

Hello Liz! Your function should have the 3 as an exponent. f(x) - 0.3(x-5)³ + 34

A = The average change with the highest change is in interval 8-10 minutes. You can actually use the function to calculate the temperatures or estimate them from the graph.

at x = 10, f(10) = 0.3(5)³ +34 = 71.5 degrees C.

at x = 8, f(8) = 0.3(3)³ +34 = 42.1 degrees C.

The average rate of change is the change in Y/Change in x.(71.5-42.1)/(10-8) = 14.7 degrees C per minute

In comparison, the interval for 0 to 2 minutes had a temperature change o 25.9 degrees C. Dividing this number by the change in time of 2 minutes gives us an average temperature change os12.95 degrees C.

B - The interval 4-6 minutes showed that the rate of temperature increase was fairly flat so this is the best answer for this part.