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: 21


(a) Trigonometric function plus a constant $$f(x)=a+b\cos x$$ (b) Linear descending function $$f(x)=-ax+b,\quad a,b>0$$

Work Step by Step

(a) The cosine function or some positive multiple of it oscillates around $x$ axis and has a maximum (one of them) when $x=0$. The data looks much like cosine function but shifted upwards which can be represented by adding a constant to a positive multiple of cosine: $$f(x)=a+b\cos x,\quad a,b>0.$$ (b) The points from the data look like they follow a line that decreases when $x$ increases so we will model with decreasing linear function of the form of $$f(x)=-ax+b, \quad a,b>0.$$ We have to take $b>0$ because the intercept with $y$ axis is positive.
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