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: 5


$$ N'(t)=\frac{\ln2}{3}N(t).$$ $$ N(t)=P_0e^{kt}=e^{t\frac{\ln 2}{3}}.$$ $$ N(60)= e^{20\ln 2}.$$

Work Step by Step

Since the doubling time is given by $\frac{\ln 2}{k}$, then we have $$3=\frac{\ln 2}{k}\Longrightarrow k=\frac{\ln2}{3}.$$ The differential equation is given by $$ N'(t)=kN(t)\Longrightarrow N'(t)=\frac{\ln2}{3}N(t).$$ When $ t=0$, we have $ P_0=N(0)=1$, then $$ N(t)=P_0e^{kt}=e^{t\frac{\ln 2}{3}}.$$ At $ t=60$, we have $$ N(60)= e^{60\frac{\ln 2}{3}}=e^{60\frac{\ln 2}{3}}=e^{20\ln 2}.$$
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