Question

A researcher fitted a function to data on how foraging rate (F, number of items consumed per 10 minutes) of a shorebird varied with its group size (G, number of individuals) and obtained the following equation:𝑙𝑜𝑔𝑒𝐹 = 3 − 0.2 × 𝑙𝑜𝑔𝑒G.According to this equation, the foraging rate (F) of a solitary forager is_________________ items per 10 minutes.(Rounded off to the nearest integer)

Hint:

Four must-know matches: \textbf{Lepidoptera} (moths/butterflies), \textbf{Coleoptera} (beetles), \textbf{Hemiptera} (true bugs), \textbf{Orthoptera} (crickets/grasshoppers).

Answer 1

Correct Answer: 19

Step 1 (Rewrite the model).
Exponentiate both sides to reveal the power-law form: \[ \log_e F = 3-0.2\log_e G \;\Rightarrow\; F = e^{\,3}\,e^{-0.2\log_e G} = e^{\,3}\,G^{-0.2}. \] Thus, \(F\) declines with group size with elasticity \(-0.2\) (a \(1\%\) increase in \(G\) reduces \(F\) by \(0.2\%\)).

Step 2 (Plug in solitary group size).
Solitary \(\Rightarrow G=1\). Note \(\log_e 1=0\) and \(1^{-0.2}=1\): \[ F=e^{3}\cdot 1 = e^{3}\approx 20.085537\ \text{items/10 min}. \]

Step 3 (Round carefully).
Nearest integer: \(F\approx \boxed{20}\) items per 10 minutes.