College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.7 - Financial Models - 6.7 Assess Your Understanding - Page 476: 62


$16.98$ years

Work Step by Step

Inflation: The amount A that ${{\$}} P$ can purchase after n years, with annual inflation rate r (decimal) is $A=P\cdot(1-r)^{n}$ --- We want n for which $A=0.5P,$, with $ r=0.04$. $0.5P=P(1-0.04)^{n} \qquad.../\div P$ $0.5=(0.96)^{n} \qquad.../\log(..)$ $\log 0.5=n\log 0.96$ $n=\displaystyle \frac{\log 0.5}{\log 0.96}\approx 16.98$ years
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