Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.1 Review of Functions - 1.1 Exercises - Page 10: 22


$d$=dependent variable $t$=independent variable Domain: [0,2]

Work Step by Step

Since the distance depends on the time elapsed, distance $d$ is the dependent variable and time $t$ is the independent variable. The domain consists of the appropriate values of $t$. The time begins with $t=0$ and ends when the stone hits the river. We can find this time by setting $d=0$: $20-5t^2=5(4-t^2)=5(2-t)(2+t)=0$ $t=2$, $t=-2$ We ignore $t=-2$, since this solution goes backwards in time. Thus the domain is [0,2]
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