October 2020 Paper 3 Q3
3 A particular phone battery will last 10 hours when it is first used. Every time it is recharged, it will only last 98% of its previous time.
Find the maximum total length of use for the battery. [3]
| Scheme | Marks | AO |
|---|---|---|
| \(10 + 10 \times 0.98 + 10 \times 0.98^2\) or \(10 + 9.8 + 9.604\) | M1 | 3.1b |
| \(\dfrac{10}{1 - 0.98}\) | M1 | 1.1 |
| 500 | A1 | 3.2a |
| [3] |
Notes
M1: Use of GP with common ratio 0.98
GP implied by formula for \(S_\infty\), \(S_n\) or \(u_n\) showing 0.98 or 1st 3 terms
M1: Sum to infinity