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.
- Initial amount of water in the bucket: 50 ml
- 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.