Question

a school is filling a tank. the graph shows the amount of water in the tank versus time (in minutes).
(a) 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 tank decreases.

at what rate is the amount of water decreasing?
square liters per minute

• as time increases, the amount of water in the tank increases.

at what rate is the amount of water increasing?
square liters per minute
(b) what is the amount of water in the tank at 0 minutes?
square liters

Explanation:

Step1: Analyze the graph's trend

Since the tank is being filled, as time (x - axis, minutes) increases, the amount of water (y - axis, liters) should increase. So the correct statement is "As time increases, the amount of water in the tank increases."

Step2: Determine the rate of increase (assuming the graph has a linear positive slope)

To find the rate, we can use the slope formula \( \text{slope}=\frac{\Delta y}{\Delta x} \). If we assume two points, say at \( x = 0 \), \( y = 0 \) (if the tank starts empty) and at \( x = 1 \), \( y = r \) (where \( r \) is the rate). But from the context of filling, the rate is positive. Let's assume the graph is linear and for example, if at \( x = 1 \) minute, \( y = 200 \) liters (estimating from typical filling graphs), but more accurately, if we take two points. Suppose the graph goes from (0,0) to (1, 200) (hypothetical for calculation), then the rate is \( \frac{200 - 0}{1 - 0}=200 \) liters per minute. But we need to check the graph. Wait, the original problem's graph: let's re - examine. The y - axis is amount of water (liters) and x - axis is time (minutes). Since it's filling, the line should have a positive slope. So the rate of increase is calculated as \( \text{rate}=\frac{\text{change in water}}{\text{change in time}} \).

Step3: Amount of water at 0 minutes

At \( t = 0 \) minutes (initial time), if the tank is being filled from empty, the amount of water is 0 liters. But we need to confirm from the graph. If the graph passes through the origin (0,0), then at 0 minutes, the amount of water is 0 liters.

Answer:

(a) Statement: "As time increases, the amount of water in the tank increases."; Rate of increase: Let's assume the graph has a slope. If we take two points, say (1, 200) and (0, 0), the rate is \( \frac{200 - 0}{1 - 0}=200 \) liters per minute (actual value depends on the graph's scale, but the process is slope calculation). (b) At 0 minutes, the amount of water is 0 liters.

(Note: Since the graph's exact scale is not fully clear, the above is a general solution based on the context of filling a tank. If the graph has specific coordinates, we can calculate more accurately. For example, if at \( x = 1 \) minute, \( y = 200 \) liters, then rate is 200 liters per minute and at \( x = 0 \), \( y = 0 \) liters.)