Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.6 Applications and Models of Exponential Growth and Decay - 4.6 Exercises - Page 479: 10

$ k=\frac{1}{6}ln(\frac{1}{3})$

Step 1. State the model equation: $y(t)=y_0e^{kt}$ Step 2. For $y_0=30\ g$ and $y(6)=10$, we have $10=30e^{6k}$ Step 3. Solve the above: $e^{6k}=\frac{1}{3}\longrightarrow 6k=ln(\frac{1}{3}) \longrightarrow k=\frac{1}{6}ln(\frac{1}{3})$