Amelia buys a new car - OCR - GCSE Maths - Question 11 - 2017 - Paper 1
Question 11
Amelia buys a new car.
The expected future value of this car, £V, is given by
$$V = 16000 imes 0.75^{i}$$
where $i$ is the age of the car in complete years.
(a... show full transcript
Worked Solution & Example Answer:Amelia buys a new car - OCR - GCSE Maths - Question 11 - 2017 - Paper 1
Step 1
Write down the value of the car when new.
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Answer
The value of the car when new is £16,000.
Step 2
Write down the annual percentage decrease in the expected value of the car.
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Answer
To find the annual percentage decrease, we note that each year, the value of the car is multiplied by 0.75. The percentage decrease per year can be calculated as:
extPercentageDecrease=(1−0.75)imes100=25%
Therefore, the annual percentage decrease in the expected value of the car is 25%.
Step 3
Show that the expected value of the car when 2 years old is £9000.
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Answer
To find the expected value when the car is 2 years old, we substitute i=2 into the formula:
V=16000imes0.752
Calculating this,
0.752=0.5625
Thus,
V=16000imes0.5625=9000
This shows that the expected value of the car when 2 years old is indeed £9000.
Step 4
Explain how you know that Amelia's graph is incorrect.
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Answer
Amelia's graph likely represents a linear decrease in value, which is incorrect. The expected value of the car decreases exponentially, not linearly. The relationship is defined by the exponential decay formula, which shows that the value drops more steeply initially and flattens out over time, not a straight line as presented in her graph.
