2025 SCGS PRELIMS P2 Q10
2025 SCGS PRELIMS P2 Q10
Secondary 4
10 marks
The number, \(n\), of a certain type of bacteria increases with time \(t\) minutes. Recorded values of \(n\) and \(t\) are shown in the table below.
| \(t\) | 2 | 4 | 6 | 8 | 10 |
| \(n\) | 3215 | 3446 | 3693 | 3959 | 4243 |
It is known that \(n\) and \(t\) are related by the formula \(n=n_0(2)^{kt}\), where \(n_0\) and \(k\) are constants.
- Explain how a straight line graph can be drawn to represent the formula and draw it for the given data.[4]
Use your graph to estimate
- the initial number of bacteria,[2]
- the value of \(k\),[2]
- the time taken for the number of bacteria to increase by 25%.[2]
Solution:
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Answer:(a) Plot \(\lg n\) against \(t\). (b) \(3000\) bacteria. (c) \(k=0.0500\). (d) \(6.44\text{ min}\).
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