Question

The profit made by a shop increases each year. The profit made by the shop in year n is £Pn Given that the profit made by the shop in the next year is £Pn + 1 then Pn + 1 = aPn + 800 where a is a constant. The table shows the profit made by the shop in 2018 and in 2019 Year 2018 2019 Profit £24 000 £29 600 Work out the profit predicted to be made by the shop in 2021

Answer 1

£44,384

Explanation:

Given the recurrence relation for profit is ...

• P[2018] = £24000
• P[2019] = £29600
• P[n+1] = a·P[n] +800

you want the profit in 2021.

Value of 'a'

Using the given relations we have ...

P[2019] = a·P[2018] +800

29600 = a·24000 +800

28800 = a·24000

a = 288/240 = 1.2

Next terms

Then the profit for the next two years is ...

P[2020] = 1.2·P[2019] +800 = 1.2·29600 +800 = 36320

P[2021] = 1.2·36320 +800 = 44384

The profit is predicted to be £44,384 in 2021.

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