Higher June 2022 Paper 3 Q20
20 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 £\(P_{n + 1}\) then
\(P_{n + 1} = aP_n + 800\) 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 (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 44 384 | P1 | for process to find \(a\), eg \(29\,600 = 24\,000a + 800\) or (\(a =\)) 1.2 oe |
| P1 | for (\(P_{2020} =\)) \(\text{``}1.2\text{''} \times 29\,600 + 800\ (= 36\,320)\) | |
| P1 | for (\(P_{2021} =\)) \(\text{``}1.2\text{''} \times \text{``}36\,320\text{''} + 800\) | |
| A1 | cao |