Exercise 1.2.35

Question

It makes sense that the larger the area of a region, the larger the number of species that inhabit the region. Many ecologists have modeled the species-area relation with a power function. In particular, the number of species $S$ of bats living in caves in central Mexico has been related to the surface area $A$ of the caves by the equation $S = 0.7A^{0.3}.$\begin{enumerate}[label=(\alph*)]
\item  The cave called 	extit{Misión Imposible} near Puebla, Mexico, has a surface area of $A = 60 m^2$. How many species of bats would you expect to find in that cave?
\item If you discover that four species of bats live in a cave, estimate the area of the cave.
\end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}
    \item For $A=60 \ m^2$, we have:
    $$S=0.7\cdot 60^{0.3}\approx 2. $$
    Thus, we're expecting to find 2 species of bats in the cave 	extit{Misión Imposible}.
    \item For $S=4,$ we have:
    $$0.7A^{0.3}=4.$$
    $$A=\sqrt[0.3]{\frac{4}{0.7}}.$$
    $$A\approx 334\mathrm{~m}^2.$$
\end{enumerate}

Exercise 1.2.35

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Exercise 1.2.35

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