Question

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Enrollment in a dance studio has grown exponentially since the studio opened. Below is a graph depicting this growth. Determine the average rate of change from x = 0 to x = 8.

A. 120
B. 0.08
C. 20
D. 12.5

Answer 1

Enrollment at X = 0 is at 20.

Enrollment at X = 8 is 120.

Find the difference between those values:

120 - 20 = 100

Divide that difference by the difference in the x values:

100 /8 = 12.5

The answer is D. 12.5

Answer 2

The average rate of change is the ratio of the change in y to the change in x values of a graph ; that is the ratio of the rise to the run. Hence, the average rate of change in growth is 12.5

• Average rate of change = Rise / Run

Rise = y2 - y1 ;

• y2 = 120
• y1 = 20
• y2 - y1 = 120 - 20 = 100

Run = x2 - x1 ;

• x2 = 8 ;
• x1 = 0
• x2 - x1 = 8 - 2 = 6

Therefore, the slope of the graph can be expressed thus :

• Slope = Rise / Run = 100 / 8 = 12.5

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