A survey finds 20 species in a plot of 10 km², and 50 species in a plot of 1000 km² in the same…

Step 1. (a) $Z = \dfrac{\log 50 - \log 20}{\log 1000 - \log 10} = \dfrac{\log 2.5}{2} = \dfrac{0.398}{2} = 0.20$.

Step 2. (b) Yes. It is in the range $0.1$ to $0.2$.

Step 3. (c) The area of $100\ \text{km}^2$ is halfway on the log scale, so the species are the geometric mean: $\sqrt{20 \times 50} = 31.6$ species.