Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 4 - Applications of the Derivative - 4.9 Antiderivatives - 4.9 Exercises: 72

Answer

$$p\left( t \right) = - 10{e^{ - t}} + 110$$

Work Step by Step

$$\eqalign{ & p'\left( t \right) = 10{e^{ - t}} \cr & p\left( t \right) = \int {p'\left( t \right)} dt \cr & then \cr & p\left( t \right) = \int {10{e^{ - t}}} dt \cr & find{\text{ the general solution}} \cr & p\left( t \right) = - 10{e^{ - t}} + C \cr & {\text{using the initial condition }}p\left( 0 \right) = 100 \cr & 100 = - 10{e^{ - 0}} + C \cr & 100 = - 10e + C \cr & C = 110 \cr & {\text{the solution to the initial value problem is}} \cr & p\left( t \right) = - 10{e^{ - t}} + 110 \cr} $$
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