Answer
Equation: $P(t)$ = $Me^{-kt}$
Work Step by Step
$\frac{dP}{dt}$ = $k(M-P)$
$\int \frac{dP}{M-P}$ = $\int kdt$
$ln(M-P(t))$ = $kt$
$M-P(t)$ = $e^{kt}$
$P(t)$ = $\frac{M}{e^{kt}}$
Thus, $P(t)$ = $Me^{-kt}$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 9 - Differential Equations - 9.3 Separable Equations - 9.3 Exercises - Page 646: 39
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