| Date | May 2008 | Marks available | 2 | Reference code | 08M.1.sl.TZ1.15 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Calculate | Question number | 15 | Adapted from | N/A |
Question
In an experiment it is found that a culture of bacteria triples in number every four hours. There are \(200\) bacteria at the start of the experiment.
Find the value of \(a\).
Calculate how many bacteria there will be after one day.
Find how long it will take for there to be two million bacteria.
Markscheme
\(a = 1800\) (A1) (C1)
[1 mark]
\(200 \times {3^6}{\text{ (or }}16200 \times 9{\text{) }} = 145800\) (M1)(A1) (C2)
[2 marks]
\(200 \times {3^n} = 2 \times {10^6}\) (where \(n\) is each \(4\) hour interval) (M1)
Note: Award (M1) for attempting to set up the equation or writing a list of numbers.
\({3^n} = {10^4}\)
\(n = 8.38{\text{ }}(8.383613097)\) correct answer only (A1)
\({\text{Time}} = 33.5{\text{ hours}}\) (accept \(34\), \(35\) or \(36\) if previous A mark awarded) (A1)(ft) (C3)
Note: (A1)(ft) for correctly multiplying their answer by \(4\). If \(34\), \(35\) or \(36\) seen, or \(32 - 36\) seen, award (M1)(A0)(A0).
[3 marks]
Examiners report
Parts (a) and (b) were answered well with most candidates attempting and gaining marks. Very few candidates gained maximum marks for part (c) with most using a list to find the number of hours rather than the formula.
Parts (a) and (b) were answered well with most candidates attempting and gaining marks. Very few candidates gained maximum marks for part (c) with most using a list to find the number of hours rather than the formula.
Parts (a) and (b) were answered well with most candidates attempting and gaining marks. Very few candidates gained maximum marks for part (c) with most using a list to find the number of hours rather than the formula.
