Question

juan is draining an aquarium. the graph shows the amount of water (in liters) in the aquarium versus time (in minutes).
amount of water (liters)
time (minutes)
(a) what is the amount of water in the aquarium at 0 minutes?
liters
(b) choose the statement that best describes how the time and amount of water are related. then fill in the blank.
as time increases, the amount of water in the aquarium
decreases.
increases.
at what rate is the amount of water decreasing?
liters per minute
at what rate is the amount of water increasing?
liters per minute

Explanation:

Step1: Analyze part (a)

To find the amount of water at 0 minutes, we look at the y - intercept of the graph. The y - axis represents the amount of water (in liters) and the x - axis represents time (in minutes). At \(x = 0\) (0 minutes), the value on the y - axis is 300 liters.

Step2: Analyze part (b) - Relationship

Since Juan is draining the aquarium, as time (x - value) increases, the amount of water (y - value) should decrease. So we choose the option "As time increases, the amount of water in the aquarium decreases".

Step3: Analyze part (b) - Rate of decrease

We can find the rate of change (slope) of the line. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). We know two points: \((0,300)\) and \((5,0)\) (assuming at 5 minutes the tank is empty, from the graph's x - intercept). So \(m=\frac{0 - 300}{5-0}=\frac{- 300}{5}=- 60\). The negative sign indicates a decrease, so the rate of decrease is 60 liters per minute.

Answer:

(a) 300 liters
(b) Statement: As time increases, the amount of water in the aquarium decreases; Rate of decrease: 60 liters per minute