the table shows the linear relationshop between the amount of water in a pool and the time the pool has been draining.

Question

Water Remaining in Pool: Time (minutes): 10, 32, 68, 90. Amount of Water (gallons): 5,385, 5,132, 4,718, 4,465.
what is the rate of change of the amount of water in the pool in gallons with respect to the number of minutes the pool has been draining?

Answer 1

To find the rate of change of the amount of water in the pool with respect to time, we will calculate the slope of the line connecting two points on the graph, using the formula for slope:

\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]

Where:

• \(y\) represents the amount of water (gallons).
• \(x\) represents the time (minutes).

Let's use the first and last points in the data:

1. \( (x_1, y_1) = (10, 5385) \)
2. \( (x_2, y_2) = (90, 4465) \)

Now plug these values into the slope formula:

\[ \text{slope} = \frac{4465 - 5385}{90 - 10} \]

Calculate the numerator and denominator separately:

• Numerator: \( 4465 - 5385 = -920 \)
• Denominator: \( 90 - 10 = 80 \)

Now find the slope:

\[ \text{slope} = \frac{-920}{80} = -11.5 \]

Thus, the rate of change of the amount of water in the pool is \(-11.5\) gallons per minute. This means that the pool is losing water at a rate of 11.5 gallons every minute.