 # The home range, in hectares, of a carnivorous mammal weighing w grams can be approximated by H(w)=0.11w^(1.36) a)Find the average rate at which a carnivorous mammal's home range increases as the animal's weight grows from 200g to 450g. b) Find (H(500)-H(400))/(500-400) , and interpret this result. skilpadw3 2022-07-25 Answered
The home range, in hectares, of a carnivorous mammal weighing w grams can be approximated by $H\left(w\right)=0.11{w}^{1.36}$
a)Find the average rate at which a carnivorous mammal's home range increases as the animal's weight grows from 200g to 450g.
b) Find $\frac{H\left(500\right)-H\left(400\right)}{500-400}$, and interpret this result.
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$H\left(w\right)=0.11{w}^{1.36}.$
$a\right)\frac{H\left(200\right)-H\left(450\right)}{200-450}=\frac{\left(148.181\right)-\left(446.439\right)}{200-450}=1.19303$
$b\right)\frac{H\left(500\right)-H\left(400\right)}{500-400}=\frac{515.219-380.36}{500-400}=1.3486$

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PART A>>>
Av rate = [ H(450) - H(200)] / (450 - 200)
= [ 446.44 - 148.18 ] / 250
= 298.26 / 250
= 1.193 hectacres/gram.
PART B>>> Av rate = [ 515.22 -380.36 ] / 100 = 134.86/100 = 1.35 hectacres/gram.

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