Chapter 5.1, Problem 52E

Time Constant Let $T$ be the time constant of the curve $y=C{e}^{-\lambda t}$ as defined in Fig. 5. Show that $T=1/\lambda$. [Hint: Express the slope of the tangent line in Fig. 5 in terms of $C$ and $T$. Then, set this slope equal to the slope of the curve $y=C{e}^{-\lambda t}$ at $t=0$]