Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.2 - Mathematical Models: A Catalog of Essential Functions. - 1.2 Exercises - Page 36: 31

Answer

(a) $N=3.105\times A^{0.308}$ For a better visualization, see the image below. (b) About 18 species.

Work Step by Step

(a) Using a power regression calculator we can estimate the average values and determine the equation of the power function. Using the calculator we will get the following: $k=3.1046204 \approx 3.105$ $n=0.3080442355 \approx 0.308$ Taking these values, we will have: $N=kA^{n}$ $N=3.105\times A^{0.308}$ (b) Using the equation calculated in (a), for $291 mi^{2}$, we will have estimated the amount of species of: $N=3.105\times 291^{0.308} \approx 17.82135$ As the amount of species can't be non-integer, we can say that $N=18$
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