Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Section 3.8 - Exponential Growth and Decay - 3.8 Exercises - Page 244: 14


The equation of the curve is: $y = 5~e^{2x}$

Work Step by Step

The slope of the curve is twice the y-coordinate: $\frac{dy}{dx} = 2y$ The solution to this equation is: $y = y(0)e^{2x}$ The curve passes through the point $(0,5)$: $y = y(0)e^{2x}$ $y(0)e^{(2)(0)} = 5$ $y(0) = 5$ The equation of the curve is: $y = 5~e^{2x}$
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