Higher November 2023 Paper 1 Q22
22. The following iterative formula can be used to find the number of cells of bacteria after \(n\) days.
\(\mathrm{B}_0 = 1000\)
\(\mathrm{B}_{n+1} = 1{\cdot}2\mathrm{B}_n\) where \(n \geqslant 0\)
(a) Show that the number of cells of bacteria after 1 day is 1200. [1]
(b) Use this formula to find the number of cells of bacteria after 3 days. [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(\mathrm{B}_1 = 1.2\times1000\ (=1200)\) | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(\mathrm{B}_2\ (= 1.2\times\mathrm{B}_1) = 1440\) | B1 | |
| \(\mathrm{B}_3 = 1.2\times\mathrm{B}_2\) or \(\mathrm{B}_3 = 1.2^2\times\mathrm{B}_1\) or \(\mathrm{B}_3 = 1.2^3\times1000\) | M1 | FT ‘their \(\mathrm{B}_2\)’ \(\times\ 1.2\) |
| 1728 oe ISW | A1 | |
| (4) |