Finding the growth constant from a second reading
Finding the growth constant from a second reading
Secondary 3
The number of bacteria, \(N\), in a culture \(t\) hours after it is set up is modelled by \(N=400\mathrm e^{kt}\). After \(5\) hours there are \(1000\) bacteria.
- Find the exact value of \(k\).
- Find the time when the number of bacteria first exceeds \(10\,000\), giving your answer correct to 3 significant figures.
- Explain why the model cannot describe the culture for very large values of \(t\).
Solution:
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Answer:(a) \(k=\tfrac15\ln2.5\) (b) \(17.6\) hours (c) \(N\) would grow without limit, which a real culture cannot do
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