Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 6 - Differential Equations - Review Exercises: 24



Work Step by Step

$(0, 5)$ lies on the curve. Thus, $$5 = Ce^{k.0}$$ Or, $$C=5$$ $(5, \frac{1}{6})$ lies on the curve. Thus, $$\frac{1}{6} = 5e^{5k}$$ Or, $$e^{5k}=\frac{1}{30}$$ $$k = \frac{\ln(1/30)}{5} = -0.68$$ So, the function is $$y=5e^{-0.68t}$$
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