The profit made by a shop increases each year. The profit made by the shop in year n is $P_n$. Given that the profit made by the shop in the next year is $P_{n+1} = a P_n + 800$ where a is a constant. The table shows the profit made by the shop in 2018 and 2019. Year 2018 2019 Profit £24000 £29600 Work out the profit predicted to be made by the shop in 2021.

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The profit made by a shop increases each year - Edexcel - GCSE Maths - Question 21 - 2022 - Paper 3

Question 21

The profit made by a shop increases each year. The profit made by the shop in year n is $P_n$. Given that the profit made by the shop in the next year is $P_{n+1} = ... show full transcript

Worked Solution & Example Answer:The profit made by a shop increases each year - Edexcel - GCSE Maths - Question 21 - 2022 - Paper 3

Step 1

Find a

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Answer

Given the profits:

For 2018 ( $P_1$ ): £24000
For 2019 ( $P_2$ ): £29600

We can set up the equation for 2019 using the formula:
$P_2 = aP_1 + 800$ Substituting the values:

$29600 = a(24000) + 800$

Now, solve for $a$ :

$29600 - 800 = 24000a$ $28800 = 24000a$ $a = \frac{28800}{24000} = 1.2$

Step 2

Calculate Profit for 2020

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Answer

Using the value of $a = 1.2$ , we can now find the profit for 2020 ( $P_3$ ):

$P_3 = aP_2 + 800$

Substituting the values:

$P_3 = 1.2(29600) + 800$ $P_3 = 35520 + 800 = 36320$

Step 3

Calculate Profit for 2021

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Answer

Now, we can find the profit for 2021 ( $P_4$ ):

$P_4 = aP_3 + 800$

Substituting the values:

$P_4 = 1.2(36320) + 800$ $P_4 = 43584 + 800 = 44384$

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