Question

(a) at what time does the amount of water in the aquarium reach 0 liters? 5 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? 90 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 Part (a)

From the graph, we look at the time when the amount of water is 0 liters. Wait, actually, the x - axis is time (minutes) and y - axis is amount of water (liters). Wait, the point on the graph: when does the amount of water reach 0 liters? Wait, maybe the graph has a point at (5, 0)? No, wait, the graph is a line. Wait, maybe the question is "At what time does the amount of water in the aquarium reach 0 liters?" From the graph, we can see that when y = 0 (amount of water is 0 liters), x (time) is 5 minutes? Wait, no, maybe I misread. Wait, the first part (a): "At what time does the amount of water in the aquarium reach 0 liters?" Looking at the graph, the line starts from (5, 0) and goes up? Wait, no, the x - axis is time (minutes) with labels 1, 2, 3, 4, 5, 6, 7, 8, 9. The y - axis is amount of water (liters) with labels 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300. Wait, the line is from (5, 0) to, say, (0, 300)? No, the slope: if at x = 5, y = 0, and as x decreases (time decreases), y increases? No, maybe the graph is of time (x) and amount of water (y), and the line is decreasing? Wait, no, the blue line: when x = 5, y = 0, and as x increases, y increases? Wait, the problem (a) is "At what time does the amount of water in the aquarium reach 0 liters?" So we need to find x when y = 0. From the graph, when y = 0, x = 5 minutes. So the answer for (a) is 5 minutes.

Step2: Analyze Part (b)

First, the statement: "As time increases, the amount of water in the aquarium decreases" is selected? No, wait, the radio button is on "As time increases, the amount of water in the aquarium decreases". Then, we need to find the rate. The rate of decrease is the slope of the line. The slope \( m=\frac{\Delta y}{\Delta x} \). Let's take two points. Let's say when x = 5, y = 0; when x = 0, y = 300? Wait, no, maybe the other way. Wait, if the line is from (0, 300) to (5, 0), then \( \Delta y=0 - 300=- 300 \), \( \Delta x = 5-0 = 5 \). So the slope is \( \frac{-300}{5}=- 60 \)? Wait, no, maybe I got the axes reversed. Wait, x - axis is time (minutes), y - axis is amount of water (liters). So if the line is decreasing, as time (x) increases, amount of water (y) decreases. So two points: let's say at x = 0, y = 300; at x = 5, y = 0. Then the change in y is \( 0 - 300=-300 \), change in x is \( 5 - 0 = 5 \). So the rate of decrease is \( \frac{\vert\Delta y\vert}{\Delta x}=\frac{300}{5}=60 \) liters per minute? Wait, no, the slope is \( \frac{\Delta y}{\Delta x}=\frac{0 - 300}{5 - 0}=- 60 \), so the rate of decrease is 60 liters per minute. Wait, but the option says "90 liters per minute" is wrong. Wait, maybe my points are wrong. Wait, the y - axis labels: 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300. So each grid is 30 liters. The x - axis: 1, 2, 3, 4, 5, 6, 7, 8, 9. So from x = 5 (y = 0) to x = 0 (y = 300), the difference in x is 5 minutes, difference in y is 300 liters. So rate is \( \frac{300}{5}=60 \) liters per minute. But the option given is "90 liters per minute" is incorrect. Wait, maybe the graph is different. Wait, the problem (b) has a blank: "At what rate is the amount of water decreasing? ____ liters per minute". Wait, maybe the correct rate is 60, but the option in the image has "90 liters per minute" as a distractor. Wait, no, maybe I misread the graph. Alternatively, if at x = 0, y = 300, and at x = 3.333, y = 0, but no, the x - axis has 5 as a label. Wait, the first part (a) answer is 5 minutes. For part (b), the statement is "As time increases, the amount of water in the aquarium decreases", and the rate is \( \frac{300}{5}=60 \) liters per minute? But the option in the image shows "90 liters per minute" as a choice? Wait, maybe the graph is from (0, 300) to (5, 0), so slope is - 60, so rate of decrease is 60 liters per minute. But maybe the problem has a typo, or I misread. Alternatively, if the y - axis is 0 to 300, and x - axis 0 to 5, then 300 liters over 5 minutes is 60 liters per minute.

Answer:

(a) 5 minutes
(b) As time increases, the amount of water in the aquarium decreases; 60 liters per minute (Note: If the graph's actual slope is 90, maybe my analysis is wrong, but based on the given axes, 300/5 = 60)