Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.6 Applications and Models of Exponential Growth and Decay - 4.6 Exercises - Page 480: 23

$9000\ yr$

Step 1. State the model equation $A(t)=A_0e^{-0.0001216t}$ (textbook page 476) Step 2. Given $A(t)=\frac{1}{3}A_0$, we have $\frac{1}{3}A_0=A_0e^{-0.0001216t}$, thus $t=\frac{1}{-0.0001216}ln(\frac{1}{3})\approx9000\ yr$