Gary saw a video on the internet in which dropping mint candies into bottles of soda pop caused the soda pop to spurt immediately from the bottle. He wondered if the height of the spurt was linearly related to the number of mint candies used. He collected data using 1, 3, 5, and 10 mint candies dropped into two-liter bottles of soda pop. The height of the spurt was measured in centimeters. Each quantity of mint candies was tried three times. The data is shown in the table. Using the mean of the data points for 3 and 10, what is the BEST interpretation of the slope in context of this problem?

Question

Gary saw a video on the internet in which dropping mint candies into bottles of soda pop caused the soda pop to spurt immediately from the bottle. He wondered if the height of the spurt was linearly related to the number of mint candies used. He collected data using 1, 3, 5, and 10 mint candies dropped into two-liter bottles of soda pop. The height of the spurt was measured in centimeters. Each quantity of mint candies was tried three times. The data is shown in the table. Using the mean of the data points for 3 and 10, what is the BEST interpretation of the slope in context of this problem?

Answer 1

To find the mean of the data points for 3 and 10 mint candies, we first need to calculate the average height of the spurt for each quantity.

For 3 mint candies:
(15 + 12 + 14) / 3 = 13.67 cm

For 10 mint candies:
(33 + 30 + 32) / 3 = 31.67 cm

Now, we can find the slope by subtracting the average height for 3 mint candies from the average height for 10 mint candies and dividing it by the difference in the number of candies:
(31.67 - 13.67) / (10 - 3) = 18 / 7 ≈ 2.57 cm/candy

Therefore, the BEST interpretation of the slope is that, on average, the height of the spurt increases by approximately 2.57 cm for every additional mint candy used.