Question

(in liters) in the aquarium versus time (in minutes).
(a) at what time does the amount of water in the aquarium reach 0 liters?
□ minutes
(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.
at what rate is the amount of water decreasing?
□ liters per minute
○ as time increases, the amount of water in the aquarium increases.
at what rate is the amount of water increasing?
□ liters per minute

Explanation:

Step1: Analyze the graph for part (a)

The graph shows the amount of water (in liters) vs. time (in minutes). We need to find when the amount of water reaches 0 liters. From the graph, we can see that the line intersects the time axis (where amount of water is 0) at \( x = 3 \) minutes? Wait, no, wait. Wait, the y - axis is amount of water (liters) and x - axis is time (minutes). Wait, looking at the graph, when time \( t = 3 \) minutes, what's the amount? Wait, maybe I misread. Wait, the problem is (a) At what time does the amount of water in the aquarium reach 0 liters? Let's assume the graph has a point where when amount is 0, time is 3? Wait, no, maybe the graph is a line. Let's think about the slope. Wait, maybe the graph is a linear graph. Let's suppose that when time \( t = 3 \) minutes, the amount of water is 0? Wait, no, maybe the x - intercept is at \( t = 3 \) minutes. So for part (a), the time when amount of water is 0 liters is 3 minutes? Wait, maybe I need to check the graph again. Wait, the user's graph: the x - axis is time (minutes) from 0 to 9, y - axis is amount of water (liters) from 0 to 600. The line starts at (3, 0) and goes up? Wait, no, the blue line: when time is 3 minutes, amount is 0? Wait, no, maybe the line is decreasing? Wait, no, the blue line: let's see, if at time \( t = 3 \) minutes, amount is 0, and as time increases, amount increases? Wait, no, the options for part (b) say "As time increases, the amount of water in the aquarium decreases" or "increases". Wait, maybe the graph is a line with x - intercept at \( t = 3 \) minutes. So for part (a), the time when amount is 0 is 3 minutes.

Step2: Analyze part (b)

We need to choose the correct statement about the relationship between time and amount of water. If the line is going from (3, 0) to, say, higher time and higher amount? No, wait, if the amount of water is increasing as time increases, but the x - intercept is at \( t = 3 \). Wait, maybe the graph is a line where when time is 0, amount is some value, and at \( t = 3 \), amount is 0. So the slope would be negative, meaning as time increases, amount of water decreases. So the correct statement is "As time increases, the amount of water in the aquarium decreases". Then, for the rate, the rate of decrease is the slope. Let's assume two points: let's say when \( t = 3 \), \( y = 0 \), and when \( t = 0 \), \( y = 180 \) (assuming the y - axis has marks). Then the slope \( m=\frac{0 - 180}{3 - 0}=\frac{- 180}{3}=- 60 \) liters per minute. So the rate of decrease is 60 liters per minute.

Step3: Solve part (a)

From the graph, the time when the amount of water is 0 liters is 3 minutes.

Step4: Solve part (b) - statement

The correct statement is "As time increases, the amount of water in the aquarium decreases" because the line has a negative slope (from the x - intercept at \( t = 3 \) and assuming a positive y - intercept at \( t = 0 \)).

Step5: Solve part (b) - rate

The rate of decrease is calculated as the change in amount of water divided by change in time. Let's take two points: (3, 0) and (0, 180) (assuming at \( t = 0 \), amount is 180 liters). Then the change in amount \( \Delta y=0 - 180=- 180 \) liters, change in time \( \Delta t = 3 - 0 = 3 \) minutes. The rate is \( \frac{\Delta y}{\Delta t}=\frac{- 180}{3}=- 60 \) liters per minute. The negative sign indicates a decrease, so the rate of decrease is 60 liters per minute.

Answer:

(a) 3 minutes
(b) Statement: "As time increases, the amount of water in the aquarium decreases."; Rate: 60 liters per minute