Magnesium-27 has a half-life of 9.45 minutes. What is the percent decay rate per minute? A half-life is the time it takes for the chemical to decay to half its current value. We are told the half-life is 9.45 minutes, which means every 9.45 minutes the amount of chemical is halved. Mathematically, repeated “halving” is the same as repeated multiplication by $\frac{1}{2}=0.5\text{.}$ We can write a formula that says, “Start with some initial amount, C, and multiply by $0.5$ every $9.45$ minutes.” $$C(0.5)^{\frac{t}{9.45}}$$ Notice we can rewrite our formula to show the “per” minute growth factor $$C(0.5)^\frac{t}{9.45}=C(0.5^\frac{1}{9.45})^{t}$$ where $$b=0.5^\frac{1}{9.45}$$ $b \approx$ (round to $3$ decimal places) From the per-minute growth factor we can calculate the percent decay per minute as $(1-{0.929277}) \cdot 100 \approx$ (Include units and round to $3$ decimal places)