Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.5 - Equations - 1.5 Exercises: 42

Answer

$i = \pm 100\sqrt {\frac{A}{P}} - 100$

Work Step by Step

$Solve$ $the$ $equation$ $for$ $the$ $indicated$ $variable:$ $A = P(1+\frac{i}{100})^2;$ $for$ $i$ Solve for $i$ Divide both sides by $P$ $\frac{A}{P} = \frac{P(1+\frac{i}{100})^2}{P}$ $\frac{A}{P} = (1+\frac{i}{100})^2$ Square root both sides $\pm \sqrt {\frac{A}{P}} = \sqrt {(1+\frac{i}{100})^2}$ $\pm \sqrt {\frac{A}{P}} = 1+\frac{i}{100}$ Subtract 1 from both sides $\pm \sqrt {\frac{A}{P}} - 1 = 1+\frac{i}{100} -1$ $\pm \sqrt {\frac{A}{P}} - 1 = \frac{i}{100}$ Multiply both sides by 100 $100(\pm \sqrt {\frac{A}{P}} - 1) = 100(\frac{i}{100})$ $i = \pm 100\sqrt {\frac{A}{P}} - 100$
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