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Part $1$

The home$$ range, in$$ hectares, of a carnivorous mammal weighing w grams can be approximated by

$$H$($w$)$equals$=0\mathrm{.}11$ w Superscript $1\mathrm{.}360\mathrm{.}11$w$1\mathrm{.}36.$

$$a$)$ Find the average rate at which a carnivorous$$ mammal's home range increases as the$$ animal's weight grows from

$550550$

g to

$800800$

g$.$

$$b$)$ Find

StartFraction Upper H left parenthesis $450$ right parenthesis minus Upper H left parenthesis $350$ right parenthesis Over $450$ minus $350$ EndFractionH$(450)$H$(350)450350,$

and interpret this result.