1. **State the problem:** We are given the half-life of a substance as 10.7 days and need to find the decay rate constant $k$. 2. **Formula used:** The decay rate constant $k$ is related to the half-life $t_{1/2}$ by the formula: $$k = \frac{\ln(2)}{t_{1/2}}$$ where $\ln(2)$ is the natural logarithm of 2. 3. **Calculate $k$:** Substitute $t_{1/2} = 10.7$ days: $$k = \frac{\ln(2)}{10.7}$$ 4. **Evaluate:** Using $\ln(2) \approx 0.693147$, $$k = \frac{0.693147}{10.7} \approx 0.064797$$ 5. **Final answer:** The decay rate constant rounded to six decimal places is $$k = 0.064797$$ This means the substance decays at a rate of approximately 0.064797 per day.