Question

the drama department recorded how long the annual school play lasted each year. length of annual school play according to the graph, when was the rate of decrease greater? between 2013 and 2016 between 2014 and 2017

Explanation:

To determine when the rate of decrease was greater, we calculate the rate of decrease for each interval by finding the change in length divided by the change in time (in years).

Step 1: Analyze the interval between 2013 and 2016

• In 2013, the length is 92 minutes.
• In 2016, the length is 80 minutes.
• Change in length: \( 80 - 92 = -12 \) minutes (negative because it's a decrease).
• Change in time: \( 2016 - 2013 = 3 \) years.
• Rate of decrease: \( \frac{\vert -12 \vert}{3} = \frac{12}{3} = 4 \) minutes per year.

Step 2: Analyze the interval between 2014 and 2017

• In 2014, the length is 90 minutes.
• In 2017, the length is 84 minutes.
• Change in length: \( 84 - 90 = -6 \) minutes (negative because it's a decrease).
• Change in time: \( 2017 - 2014 = 3 \) years.
• Rate of decrease: \( \frac{\vert -6 \vert}{3} = \frac{6}{3} = 2 \) minutes per year.

Step 3: Compare the rates of decrease

The rate of decrease between 2013 and 2016 is 4 minutes per year, and between 2014 and 2017 is 2 minutes per year. Since \( 4 > 2 \), the rate of decrease is greater between 2013 and 2016.

Answer:

between 2013 and 2016