College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding: 93

Answer

$y=Ce^{-4x}+3$

Work Step by Step

Subtract by $\ln{C}$ on both sides: $\ln{(y-3)} - \ln{C}=-4x$ RECALL: For positive real numbers M and N: $\ln{M} - \ln{N} = \ln{\left(\dfrac{M}{N}\right)}$ Use the rule above to obtain: $\ln{\left(\dfrac{y-3}{C}\right)}=-4x$ RECALL: $\ln{M}= y \longrightarrow e^y=M$ Use the rule above to obtain: $e^{-4x}=\dfrac{y-3}{C}$ Multiply by $C$ on both sides of the equation to obtain: $C \cdot e^{-4x} = C \cdot \dfrac{y-3}{C} \\Ce^{-4x} = y-3 \\y-3=Ce^{-4x}$ Add $3$ to both sides of the equation to obtain: $y-3+3 = Ce^{-4x}+3 \\y=Ce^{-4x}+3$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.