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A made-up laboratory counts 200, 400, 800 and 1600 bacteria at 0, 2, 4 and 6 hours…

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

A made-up laboratory counts $200$ , $400$ , $800$ and $1600$ bacteria at $0$ , $2$ , $4$ and $6$ hours. Find $\log_{10}$ of the count at $4$ hours, to three decimal places. Find the slope of the straight line through the four points ( $\log_{10}$ of the count against time), to four decimal places, and the doubling time in hours.

Need a reminder? The key ideaShow

Growth by an equal factor each step is a straight line on a log scale: $\log_{10} y = a + bx$ , with a factor of $10^{b}$ per unit of $x$ and a doubling time of $\dfrac{\log_{10} 2}{b}$ . A square root straightens a quantity that grows like a square.

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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