Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.4 - Exponential and Logarithmic Equations - Exercise Set - Page 489: 110

Answer

$4.0$

Work Step by Step

Solve the given formula for $ t.$ $ A=P(1+\displaystyle \frac{r}{n})^{nt}\quad $ ... $/\div P $ $(A/P)=(1+\displaystyle \frac{r}{n})^{nt}\quad $ ... $/\ln(...)$ $\displaystyle \ln(A/P)=nt\ln(1+\frac{r}{n})\quad $ ... $/\displaystyle \times\frac{1}{n\ln(1+\frac{r}{n})}$ $ t=\displaystyle \frac{\ln(A/P)}{n\ln(1+\frac{r}{n})}$ Insert $ P=5000, \ n=365, \ r=0.147, \ A=9000$ $ t=\displaystyle \frac{\ln(9000/5000)}{365\cdot\ln(1+\frac{0.147}{365})} \approx 3.999$ (round to 1 dec. place)
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