Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.2 Mathematical Models: A Catalog of Essential Functions - 1.2 Exercises - Page 36: 32


(a) $T = d^{1.5}$ (b) Yes.

Work Step by Step

(a) Using technology, a power model with the form $T = ad^b$ with $a=1.00043122$ and $b = 1.49952874$ which are rounded to $a=1$ and $1.5$. This results in the equation: $T = d^{1.5}$ (b) The model corroborates Kepler's Third Law since the law can be expressed as follows: $T^2$ $\alpha$ $d^3$ or $T^2 = kd^3$ (where k is some constant) which, when simplified becomes: $T = k^{0.5}d^{1.5}$ Which is equivalent to the power model in (a), where k is approximately 1.
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