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: 22

Answer

(a) We model with $$f(x)=a b^x, \quad a>0,\quad b>1.$$ (b) We model with $$f(x)=\frac{a}{x},\quad a>0.$$

Work Step by Step

(a) The points from the data look like some exponential growth. The exponential function will grow if the basis is greater than one and if the multiplying constant is positive so we have $$f(x)=a b^x,\quad a>0,\quad b>1.$$ (b) These points look like they follow a hyperbola that has both $x$ and $y$ axes as asymptotes. The general equation for such hyperbola is given by $$f(x)=\frac{a}{x},\quad a>0,$$ and we will take it as the model for the given data.
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