Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.12 - Modeling Variation - 1.12 Exercises - Page 127: 20

Answer

$w=\dfrac{24}{t}$

Work Step by Step

$w$ is inversely proportional to $t$ so the equation that relates the variables is: $w=\dfrac{k}{t}$ where k = constant of proportionality. If t = 8, then w = 3. Substitute these values into the equation above to have: $w=\dfrac{k}{x} \\3 = \dfrac{k}{8} \\3(8)=k \\24=k$ The constant of proportionality is $24$. Thus, the equation that relates w and t is: $w=\dfrac{24}{t}$
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