Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.5 Compound Interest and Present Value - Exercises - Page 355: 4

Answer

$$t \approx 9.90\ \ \ \text{years }$$

Work Step by Step

Given $$ P_0=4000,\ \ \ \ \ r=0.07 $$ We use the compound interest formula: \begin{align*} P(t)&=4000 e^{0.07 \cdot t}\\ 8000&=4000 e^{0.07 \cdot t}\\ 2&=e^{0.07 \cdot t}\\ \ln 2&=0.07 t \end{align*} Hence $$t \approx 9.90\ \ \ \text{years }$$
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