Answer
a. $S = \frac {c}{A^k}$
b. See explanation below
Work Step by Step
Given $\log S = \log c + k \log A$
a. Solve for S
$\log S = \log c + \log A^k$
$\log S = \log (\frac {c}{A^k})$
$S = \frac {c}{A^k}$
b. k = 3, prove doubling the area increases the number of species by eightfold
$S = \frac {c}{(2A)^3}$
$8S = \frac{c}{A}$
Thus the number of species increases by eightfold.
