1. **State the problem:** We need to find the decay rate of Turenchalkygen-62, an isotope with a half-life of 170 days, using the equation $y = ae^{kt}$ where $k$ is the decay constant. 2. **Recall the formula for half-life:** The half-life $T_{1/2}$ is related to the decay constant $k$ by the formula: $$T_{1/2} = \frac{\ln(2)}{|k|}$$ 3. **Rearrange to find $k$:** $$|k| = \frac{\ln(2)}{T_{1/2}}$$ 4. **Substitute the half-life value:** $$|k| = \frac{\ln(2)}{170}$$ 5. **Calculate the numerical value:** $$|k| = \frac{0.693147}{170} \approx 0.0040779$$ 6. **Interpretation:** Since this is a decay process, $k$ is negative: $$k \approx -0.0040779$$ 7. **Round to the nearest thousandth:** $$k \approx -0.004$$ **Final answer:** The decay rate constant $k$ for Turenchalkygen-62 is approximately $-0.004$ per day.