Question

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)
Responses

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 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 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.

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.
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Answer 1

To determine which graph accurately represents the amount of water in the leaky bucket over time, we need to establish a mathematical model based on the information provided.

1. **Initial amount of water in the bucket**: 50 ml
2. **Rate of water loss**: 15 ml every 4 minutes

The rate of water loss can be converted to a per-minute basis:
- Water loss rate: \( \frac{15 \text{ ml}}{4 \text{ min}} = 3.75 \text{ ml/min} \)

Now, we can express the amount of water \( W(t) \) in the bucket at any time \( t \) (in minutes) using the formula:
\[
W(t) = 50 - 3.75t
\]

We can now calculate the water volume at specific time intervals:

- At \( t = 0 \):
\[
W(0) = 50 - 3.75 \times 0 = 50 \text{ ml}
\]
- At \( t = 4 \):
\[
W(4) = 50 - 3.75 \times 4 = 50 - 15 = 35 \text{ ml}
\]
- At \( t = 8 \):
\[
W(8) = 50 - 3.75 \times 8 = 50 - 30 = 20 \text{ ml}
\]
- At \( t = 12 \):
\[
W(12) = 50 - 3.75 \times 12 = 50 - 45 = 5 \text{ ml}
\]

With this information, we identify the points we have:
- At \( t = 0 \): \( 50 \) ml
- At \( t = 4 \): \( 35 \) ml
- At \( t = 8 \): \( 20 \) ml
- At \( t = 12 \): \( 5 \) ml

Looking at the graph options you provided, the second graph is the only one that corresponds with these values:
- At \( t = 0 \): \( (0, 50) \)
- At \( t = 4 \): \( (4, 35) \)
- At \( t = 8 \): \( (8, 20) \)

Thus, the answer is the second graph.