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A culture of bacteria has 500 cells. It grows exponentially with r = 0.2 for each cell in an hour…

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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 culture of bacteria has $500$ cells. It grows exponentially with $r = 0.2$ for each cell in an hour.

How many cells are there after $3$ hours? Use $e^{0.6} = 1.822$ .

What would be the number after $3$ hours if the growth were a straight line, $N_0(1 + rt)$ ?

Which of the two is larger? Why?

Need a reminder? The key ideaShow

Exponential growth: $N_t = N_0 e^{rt}$ , with $r = b - d$ . Logistic growth: $\dfrac{dN}{dt} = rN\dfrac{K - N}{K}$ , with the largest rate $rK/4$ at $N = K/2$ . Life history: some species breed once, others many times. Some have many small offspring, others few large ones.

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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