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 34: 16


(a) $d = 48t$ (b) See image for graph (c) The slope of this line represents the constant speed at which Jason travelled.

Work Step by Step

(a) To express distance travelled as a function of time elapsed, we multiply speed with time to get distance, or: $d = vt$ Where $v$ is speed. Rearranging the equation and inputting values from the problem gives: $v = \frac{d}{t}$ $v = \frac{40}{50/60}$ (where 50/60 is the fraction of an hour it took to travel) $v = 48$ mph Inputting this value in the original equation gives: $d = 48t$ (b) Graph a linear function with $m=48$ and $b=0$ by plotting two points and joining them. (c) The slope represents the constant speed at which Jason travelled, as shown in the explanation for (a). It is a constant speed and not simply an average speed since it is stated explicitly in the question that it was constant.
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