Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.6 Applications and Models of Exponential Growth and Decay - 4.6 Exercises - Page 479: 12

$ k=\frac{1}{200}ln(\frac{1}{2})$

Step 1. State the model equation: $y(t)=y_0e^{kt}$ Step 2. For $y_0=20\ mg$ and $y(200)=20/2=10$, we have $10=20e^{200k}$ Step 3. Solve the above: $e^{200k}=\frac{1}{2}\longrightarrow 200k=ln(\frac{1}{2}) \longrightarrow k=\frac{1}{200}ln(\frac{1}{2})$