A population grows logistically with r = 0.4 for each individual in a year and K = 1000…

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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 population grows logistically with $r = 0.4$ for each individual in a year and $K = 1000$ .

What is its growth rate when $N = 50$ ?

What is its growth rate when $N = 500$ ?

What is its growth rate when $N = 900$ ?

What is the largest growth rate, and at which $N$ is it reached?

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

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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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