Chapter 3 - Section 3.1 - Derivatives of Polynomials and Exponential Functions - 3.1 Exercises - Page 182: 56

$0.359$

$\frac{dS}{dA}=(0.882)(0.842)A^{0.842-1}=0.742644A^{-0.158}$ When $A=100$, $\frac{dS}{dA}=0.742644(100)^{-0.158}=0.359$ This means when the area is $100$ square meters, the number of species in the region is increasing at a rate of species per square meter.