Question

a bathtub that contains 20 gallons of water drains at a steady rate. the graph shows the amount of water in the tub, $y$, as a function of the number of minutes the tub drains, $x$.
use the graph to describe the function.
the initial value is 20 .
it represents the amount of water in the tub before it starts to drain .
e $y$-values decrease as the values increase, so the function s a negative rate of change.
ount of water decreases by ? gallons each minute the tub drains.
the rate of change is ? .

Explanation:

Step1: Identify total change in water

Initial water: $y_1=20$ gal, final water: $y_2=0$ gal.
Change in water: $\Delta y = y_2 - y_1 = 0 - 20 = -20$ gal

Step2: Identify total change in time

Start time: $x_1=0$ min, end time: $x_2=4$ min.
Change in time: $\Delta x = x_2 - x_1 = 4 - 0 = 4$ min

Step3: Calculate rate of change

Rate of change = $\frac{\Delta y}{\Delta x}$
$\text{Rate of change} = \frac{-20}{4} = -5$
The negative sign means water decreases by 5 gallons per minute.

Answer:

The amount of water decreases by 5 gallons each minute the tub drains.
The rate of change is -5.