Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.4 - The Chain Rule - 3.4 Exercises - Page 206: 89

Answer

(a) $Q(t) = 100.0124369\cdot e^{-10.00553063~t}$ (b) The current at $~~t = 0.04~s~~$ is $~~-670.6~\mu A$

Work Step by Step

(a) An exponential regression function gives us the following exponential model for the charge: $Q(t) = 100.0124369\cdot e^{-10.00553063~t}$ (b) We can find the current when $t = 0.04~s$: $Q(t) = 100.0124369\cdot e^{-10.00553063~t}$ $Q'(t) = (100.0124369)(-10.00553063)\cdot e^{-10.00553063~t}$ $Q'(0.04) = (100.0124369)(-10.00553063)\cdot e^{(-10.00553063)~(0.04)}$ $Q'(0.04) = -670.6~\mu A$ In Example 2.1.2, the current at $~~t = 0.04~s~~$ was estimated to be $~~-670~\mu A~~$ which is very close to the result we found with the exponential model.
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