Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.4 Exponential Growth and Decay - Exercises - Page 349: 9


$$ y= 1000 e^{3t-6}.$$

Work Step by Step

The solution of the differential equation is given by $$ y=Ce^{3t}.$$ To find $ C $, we use the initial condition $ y(2)=1000$, then we have $ C=1000 e^{-6}$. Hence the solution is $$ y=1000 e^{-6}e^{3t}=1000 e^{3t-6}.$$
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