College Algebra (10th Edition)

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

Chapter 6 - Section 6.6 - Logarithmic and Exponential Equations - 6.6 Assess Your Understanding - Page 467: 108

Answer

a) After almost 2 years. b) After almost 6 and a half years. c) After a little more than 9 years.

Work Step by Step

a) Replace V(t) with 16,000 and solve for t: $16,000=18,955(0.905)^{t}$ $\dfrac{16,000}{18,955}=0.905^{t}$ $t=\log_{0.905}\dfrac{16,000}{18,955}$ $t=\dfrac{\log\frac{16,000}{18,955}}{\log0.905}$ $t\approx\dfrac{-0.0736}{-0.0434}$ $t\approx1.7$ b) Replace V(t) with 10,000 and solve for t: $10,000=18,955(0.905)^{t}$ $\dfrac{10,000}{18,955}=0.905^{t}$ $t=\log_{0.905}\dfrac{10,000}{18,955}$ $t=\dfrac{\log\frac{10,000}{18,955}}{\log0.905}$ $t\approx\dfrac{-0.2777}{-0.0434}$ $t\approx6.4$ c) Replace V(t) with 7500 and solve for t: $7500=18,955(0.905)^{t}$ $\dfrac{7500}{18,955}=0.905^{t}$ $t=\log_{0.905}\dfrac{7500}{18,955}$ $t=\dfrac{\log\frac{7500}{18,955}}{\log0.905}$ $t\approx\dfrac{-0.4027}{-0.0434}$ $t\approx9.3$
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