The price of a seat on a flight, £P, is given by P = 49 × 1.009ⁿ where n is the number of seats already sold on this flight. (a) Write down the percentage increase in price of the second seat sold compared to the first seat sold. (b) Show that the price of the 40th seat sold is less than £70.

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The price of a seat on a flight, £P, is given by P = 49 × 1.009ⁿ where n is the number of seats already sold on this flight - OCR - GCSE Maths - Question 16 - 2023 - Paper 6

Question 16

The price of a seat on a flight, £P, is given by P = 49 × 1.009ⁿ where n is the number of seats already sold on this flight. (a) Write down the percentage increas... show full transcript

Worked Solution & Example Answer:The price of a seat on a flight, £P, is given by P = 49 × 1.009ⁿ where n is the number of seats already sold on this flight - OCR - GCSE Maths - Question 16 - 2023 - Paper 6

Step 1

Write down the percentage increase in price of the second seat sold compared to the first seat sold.

96%

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Answer

To find the price of the first and second seats sold:

For the first seat (n=0): $P_1 = 49 \times 1.009^0 = 49 \times 1 = £49$
For the second seat (n=1): $P_2 = 49 \times 1.009^1 = 49 \times 1.009 ≈ £49.441$

Now, calculate the percentage increase:

$\text{Percentage Increase} = \left( \frac{P_2 - P_1}{P_1} \right) \times 100$

$\text{Percentage Increase} = \left( \frac{49.441 - 49}{49} \right) \times 100 ≈ 0.897\%$

Step 2

Show that the price of the 40th seat sold is less than £70.

99%

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Answer

To find the price of the 40th seat sold (n=39):

$P_{40} = 49 \times 1.009^{39}$

First, calculate the exponent:

$1.009^{39} ≈ 1.360127$

Now substitute this back into the price formula:

$P_{40} ≈ 49 \times 1.360127 ≈ 66.22523$

Since £66.22523 < £70, we conclude that the price of the 40th seat sold is indeed less than £70.

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