Explanation Given information: An island of A square kilometres in the Florida Keys has N species of beetles is given by N = f ( A ) = 8.3 A 0.25 . Formula used: d d x ( x n ) = n x n − 1 Calculation: N = f ( A ) = 8.3 A 0.25 (Given) Differentiating with respect to ‘ A’, we get d N d A = f ' ( A ) = d d A ( 8.3 A 0.25 ) = 8.3 d d A ( A 0 To determine (b) To find and interpret: f ( 40 ) a n d f ' ( 40 ) To determine (c) To interpret: f ( 40 ) in terms of beetles and Key Largo. To determine (d) To interpret: f ' ( 40 ) in terms of Key Largo, shrinking land mass and beetles.

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Differential Equations

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Chapter 3.1, Problem 68P

To determine

(a)

To find:

f'(A)

To determine

(b)

To find and interpret:

f(40) and f'(40)

To determine

(c)

To interpret:

f(40) in terms of beetles and Key Largo.

To determine

(d)

To interpret:

f'(40) in terms of Key Largo, shrinking land mass and beetles.

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Chapter 3.1, Problem 67P

Chapter 3.1, Problem 69P

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(a) To find: f ' ( A )

Solution Summary: The author calculates that an island of A square kilometres in the Florida Keys has N species of beetles, based on N=f(A)=8.3A0.25.

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(a)

To find:

f'(A)

(b)

To find and interpret:

f(40) and f'(40)

(c)

To interpret:

f(40) in terms of beetles and Key Largo.

(d)

To interpret:

f'(40) in terms of Key Largo, shrinking land mass and beetles.

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Chapter 3 Solutions

(a) To find: f ' ( A )

Solution Summary: The author calculates that an island of A square kilometres in the Florida Keys has N species of beetles, based on N=f(A)=8.3A0.25.

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(a) To find: f'(A)

(b) To find and interpret: f(40) and f'(40)

(c) To interpret: f(40) in terms of beetles and Key Largo.

(d) To interpret: f'(40) in terms of Key Largo, shrinking land mass and beetles.

Want to see the full answer?

Chapter 3 Solutions

(a)

To find:

f'(A)

(b)

To find and interpret:

f(40) and f'(40)

(c)

To interpret:

f(40) in terms of beetles and Key Largo.

(d)

To interpret:

f'(40) in terms of Key Largo, shrinking land mass and beetles.