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The graph below gives the volume, in litres, of water in a container / seconds after the water starts to fill the container - Edexcel - GCSE Maths - Question 21 - 2022 - Paper 2
Question 21
The graph below gives the volume, in litres, of water in a container / seconds after the water starts to fill the container. (a) Calculate an estimate for the gradi... show full transcript
Worked Solution & Example Answer:The graph below gives the volume, in litres, of water in a container / seconds after the water starts to fill the container - Edexcel - GCSE Maths - Question 21 - 2022 - Paper 2
Step 1
Calculate an estimate for the gradient of the graph when t = 17.5
Answer
To calculate the gradient at t = 17.5 seconds, we need to find two points on the graph surrounding this time point:
- Identify the volume at t = 15 seconds, which appears to be approximately 12 litres.
- Identify the volume at t = 20 seconds, which seems to be around 20 litres.
Using the formula for the gradient:
We calculate the change in volume:
- Change in Volume = Volume at t = 20 seconds - Volume at t = 15 seconds = 20 - 12 = 8 litres.
The change in time:
- Change in Time = 20 - 15 = 5 seconds.
Now, substituting these values into the gradient formula:
Thus, the estimated gradient of the graph when t = 17.5 seconds is approximately 1.6 litres per second.
Step 2
Describe fully what the gradient in part (a) represents
Answer
The gradient calculated in part (a) represents the rate of change of volume of water in the container with respect to time. Specifically, it indicates how many litres of water are added to the container per second when the time is approximately 17.5 seconds. A gradient of 1.6 litres/second means that at that moment, the water volume is increasing at a rate of 1.6 litres for every second that passes.