1. The problem asks to find the decay rate constant $k$ for a substance with a half-life of 12.9 days. 2. The formula relating half-life $t_{1/2}$ and decay rate $k$ is: $$t_{1/2} = \frac{\ln(2)}{k}$$ where $\ln(2)$ is the natural logarithm of 2. 3. To find $k$, rearrange the formula: $$k = \frac{\ln(2)}{t_{1/2}}$$ 4. Substitute $t_{1/2} = 12.9$ days: $$k = \frac{\ln(2)}{12.9}$$ 5. Calculate $\ln(2) \approx 0.693147$: $$k = \frac{0.693147}{12.9} \approx 0.053740$$ 6. Rounded to six decimal places, the decay rate constant is: $$k = 0.053740$$ This means the substance decays at a rate of approximately 0.053740 per day.