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) (i... 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
The annual percentage decrease can be calculated as follows:
The depreciation factor is 0.75, so the annual percentage decrease is:
100imes(1−0.75)=25%
Thus, 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 value of the car when it is 2 years old, we use the formula:
V=16000imes0.752
Calculating this gives:
V=16000imes0.5625=9000
Thus, 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 is incorrect because it suggests that the value of the car decreases linearly over time, while in reality, the expected value follows an exponential decay function due to the multiplicative factor in the formula. As the car ages, its value does not decrease by a constant amount each year, but rather by a constant percentage, leading to a curve that flattens over time rather than a straight line.
