The price, £P, of a car is £20,000 in 2019 - OCR - GCSE Maths - Question 12 - 2020 - Paper 1
Question 12
The price, £P, of a car is £20,000 in 2019.
The price is expected to decrease by 5% each year after 2019.
(a) Jasmine says
This means the price in 2021 is expected... show full transcript
Worked Solution & Example Answer:The price, £P, of a car is £20,000 in 2019 - OCR - GCSE Maths - Question 12 - 2020 - Paper 1
Step 1
Her error is
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Answer
Jasmine's error lies in her calculation of the price for 2021. She assumes a simple subtraction to find the price, instead of accounting for the compounded nature of the price decrease. In reality, the price decreases by 5% each year, meaning we multiply the previous year's price by 0.95 (which is equivalent to a 5% decrease).
Step 2
The correct answer is
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Answer
To find the price in 2021, we need to take the 2019 price of £20,000 and apply the 5% decrease for two years:
For 2020:
P(2020)=20000imes0.95=£19000
For 2021:
P(2021)=19000imes0.95=£18050
Thus, the correct answer is £18050.
Step 3
(b) (i) Write a formula for P in terms of n
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Answer
The formula for the price P in terms of n (the number of years after 2019) can be expressed as:
P(n)=20000imes(0.95)n
Step 4
(b)(ii) Circled graph
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Answer
The graph that best represents the price, £P, of the car as n years after 2019 would show a continuously decreasing function, likely following an exponential decay pattern.
