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: 23

Answer

$A=\dfrac{18x}{t}$

Work Step by Step

$A$ is directly proportional to $x$ and inversely proportional to $t$ so the equation that relates the variables is: $A=k \cdot \frac{x}{t}$ where k = constant of proportionality. If x = 7 and t = 3, then A = 42. Substitute these values into the equation above to have: $A=k \cdot \frac{x}{t} \\42 = k \cdot \frac{7}{3} \\42=\frac{7k}{3} \\3(42)=7k \\126=7k \\\frac{126}{7}=k \\18=k$ The constant of proportionality is $18$. Thus, the equation that relates A, x and t is: $A=18 \cdot \frac{x}{t} \\A=\frac{18x}{t}$
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