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A leaky bucket contains 50 ml of water and is losing water at a rate of 15 ml of water every 4 minutes. Select the graph that shows how much water will be in the bucket over time.(1 point)

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A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 2 comma 20 right parenthesis, left parenthesis 4 comma 30 right parenthesis, and left parenthesis 6 comma 40 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 2 comma 20 right parenthesis, left parenthesis 4 comma 30 right parenthesis, and left parenthesis 6 comma 40 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: left parenthesis 0 comma 50 right parenthesis, left parenthesis 4 comma 35 right parenthesis, and left parenthesis 8 comma 20 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: left parenthesis 0 comma 50 right parenthesis, left parenthesis 4 comma 35 right parenthesis, and left parenthesis 8 comma 20 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 40 in increments of 10 and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: left parenthesis 0 comma 50 right parenthesis, left parenthesis 20 comma 35 right parenthesis, and left parenthesis 40 comma 20 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 40 in increments of 10 and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: left parenthesis 0 comma 50 right parenthesis, left parenthesis 20 comma 35 right parenthesis, and left parenthesis 40 comma 20 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 50 in increments of 10 and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 0 right parenthesis, left parenthesis 10 comma 10 right parenthesis, left parenthesis 20 comma 20 right parenthesis, and left parenthesis 30 comma 30 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 50 in increments of 10 and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 0 right parenthesis, left parenthesis 10 comma 10 right parenthesis, left parenthesis 20 comma 20 right parenthesis, and left parenthesis 30 comma 30 right parenthesis. A solid arrow passes through these points.
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1 answer

To determine the correct graph that represents how much water is in the leaky bucket over time, we start with the relevant information:

  1. The bucket initially contains 50 ml of water.
  2. It loses water at a rate of 15 ml every 4 minutes.

First, let's calculate the rate of loss in milliliters per minute:

\[ \text{Rate of loss} = \frac{15 \text{ ml}}{4 \text{ minutes}} = 3.75 \text{ ml/minute} \]

Now, we can create a formula for the amount of water \( W(t) \) in the bucket at time \( t \) minutes:

\[ W(t) = 50 - 3.75t \]

Next, we can plug in some values for \( t \) to see how the water level changes:

  • At \( t = 0 \) minutes: \[ W(0) = 50 - 3.75(0) = 50 \text{ ml} \]

  • At \( t = 4 \) minutes: \[ W(4) = 50 - 3.75(4) = 50 - 15 = 35 \text{ ml} \]

  • At \( t = 8 \) minutes: \[ W(8) = 50 - 3.75(8) = 50 - 30 = 20 \text{ ml} \]

  • At \( t = 12 \) minutes: \[ W(12) = 50 - 3.75(12) = 50 - 45 = 5 \text{ ml} \]

According to this information, the water level should decrease from 50 ml at \( t = 0 \) to 35 ml at \( t = 4 \), to 20 ml at \( t = 8 \), and continue to decrease.

Now looking at the graph options:

  1. The first graph has points at (0, 10), (2, 20), (4, 30), and (6, 40) which do not match the calculated values.
  2. The second graph has points at (0, 50), (4, 35), and (8, 20). This matches the calculated values.
  3. The third graph has points at (0, 50), (20, 35), and (40, 20), but does not correspond to the calculated intervals properly.
  4. The fourth graph starts from (0, 0) and does not match the start of 50 ml.

Therefore, the correct graph that shows how much water will be in the bucket over time is the second option:

  • Point (0, 50) at \( t = 0 \)
  • Point (4, 35) at \( t = 4 \)
  • Point (8, 20) at \( t = 8 \)

This clearly indicates a decrease in water volume consistent with the calculated values.