Question

Time
(in minutes) Depth
(in cm)
2 47
4 41
6 38
8 37
10 32
12 24
14 20
16 19
18 13
20 8
22 7
1. Emily measured the depth of water in a bathtub at two-minute intervals after the tap was turned off and the stopper released. The table shows her data.
a) Make a scatter plot for the data.
b) Describe the correlation of the scatter plot.
c) What will the approximate depth be at 15 seconds?

Answer 1

a) To make a scatter plot for the data, we will place the time values on the x-axis and the depth values on the y-axis. Each point on the scatter plot will represent a pair of time and depth values.

b) The scatter plot shows a negative correlation. As time increases, the depth of water decreases.

c) To approximate the depth at 15 seconds, we can extrapolate from the scatter plot. Since 1 minute is equal to 60 seconds, we can estimate that 15 seconds is approximately 1/4th of a minute. From the scatter plot, it appears that the depth decreases by about 10 cm every 2 minutes. Therefore, in 1/4th of a minute (15 seconds), the depth will decrease by about 1/8th of the amount it decreases in 2 minutes, which is approximately 1.25 cm.

So, the approximate depth at 15 seconds will be 20 cm - 1.25 cm = 18.75 cm.