## University Calculus: Early Transcendentals (3rd Edition)

The exponential growth can be written as: $y=y_0e^{-kt}$ ...(1) This implies that $y=y_0e^{-k(3/k)} \implies y=y_0e^{-3}$ we can see that $y=\dfrac{y_0}{e^{3}} \lt \dfrac{y_0}{20}$ or, $\dfrac{y_0}{e^{3}} \lt (0.05)y_0$ Hence, we conclude that after three mean lifetimes we are left with 5% and so, more than 95% disintegrates.