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Aditi plots ln N against t in minutes for a culture with a doubling time of 40 min.

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Aditi plots $\ln N$ against $t$ in minutes for a culture with a doubling time of $40$ min. Show that the points lie on a straight line, and find its slope. What would the slope be for a doubling time of $20$ min?

Need a reminder? The key ideaShow

Exponential growth: $N = N_0 \times 2^{t/T}$ , with doubling time $T$ , or $N = N_0 e^{rt}$ , with growth rate $r$ . They agree when $T = \dfrac{\ln 2}{r}$ . In Python: N0 * 2 ** (t / T) and N0 * np.exp(r * t); a loop doubles with N = 2 * N. On a log axis the growth is a straight line.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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