It has been shown that the home range, in hectares, of a carnivorous mammal weighing w grams can be approximated by
$H(w)=0.11 w^{1.36}.$
(Source: Based on information in Emlen, J. M., Ecology: An Evolutionary Approach, p. 200, Reading, MA: AddisonWesley, $1973 ;$ and Harestad, $A$. S., and Bunnel, $\mathrm{F}$. . " Home Range and Body Weight- - $\Lambda$ Recvaluation," Ecology, Vol. $60, \text { No. } 2, \text { pp. } 389-402 .)$
a) Find the average rate at which a carnivorous mammals home range increases as the animal's weight grows Irom $500 \mathrm{g}$ to $700 \mathrm{g}.$
b) Find $\frac{H(300)-H(200)}{300-200},$ and interpret this result.