Calculus 10th Edition

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

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.4 Exercises - Page 352: 27

Answer

(a)

Work Step by Step

$y=C(1-e^{-ax})$ or $y=C-Ce^{a(-x)}$ which can be broken down into three transformations in $ y=e^x$ 1) x→-ax (Reflection in the y-axis and scale change of x-axis) Now our equation is $ y=e^{-ax}$ 2)y→-y/C (Reflection in the x-axis and scale change of y-axis) Now our equation is $ y=-Ce^{-ax}$ 3)y→y-C (Vertical shift of C units) Thus the final graph will match closely with the option (a). Also, note that the graph is asymptotic to the equation y=C
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