The graph gives the volume of water, in litres, in a container at time t seconds after the water started to flow out of the container - Edexcel - GCSE Maths - Question 16 - 2021 - Paper 3
Question 16
The graph gives the volume of water, in litres, in a container at time t seconds after the water started to flow out of the container.
Using the graph, work out an ... show full transcript
Worked Solution & Example Answer:The graph gives the volume of water, in litres, in a container at time t seconds after the water started to flow out of the container - Edexcel - GCSE Maths - Question 16 - 2021 - Paper 3
Step 1
Using the graph at t = 12
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Answer
To estimate the rate at which water is flowing out when ( t = 12 ), we first identify the volume of water at ( t = 12 ) seconds from the graph.
From the graph, the volume at ( t = 12 ) is approximately 30 litres.
Step 2
Finding the volume at t = 11 and t = 13
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Answer
Next, we need to find the volume of water at ( t = 11 ) seconds and ( t = 13 ) seconds to estimate the rate of change.
Assuming from the graph,
Volume at ( t = 11 ) is approximately 34 litres.
Volume at ( t = 13 ) is approximately 28 litres.
Step 3
Calculating the rate of change
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Answer
We can now compute the average rate of change of volume over the interval from ( t = 11 ) to ( t = 13 ):
[
\text{Rate} = \frac{\text{Change in Volume}}{\text{Change in Time}} = \frac{28 - 34}{13 - 11} = \frac{-6}{2} = -3 \text{ litres per second}
]
Thus, the estimated rate at which the water is flowing out of the container at ( t = 12 ) seconds is approximately 3 litres per second.
