1. **State the problem:** A doctor prescribes 550 mg of a drug, and after 4 hours, 330 mg remains. We need to find the decay factor. 2. **Formula used:** The amount of drug remaining after time $t$ can be modeled by exponential decay: $$ A = A_0 \times b^t $$ where: - $A_0$ is the initial amount (550 mg), - $A$ is the amount remaining after time $t$ (330 mg), - $b$ is the decay factor per hour, - $t$ is the time elapsed (4 hours). 3. **Set up the equation:** $$ 330 = 550 \times b^4 $$ 4. **Isolate $b^4$:** $$ b^4 = \frac{330}{550} $$ 5. **Simplify the fraction:** $$ b^4 = \frac{\cancel{330}}{\cancel{550}} = \frac{3}{5} = 0.6 $$ 6. **Solve for $b$ by taking the fourth root:** $$ b = \sqrt[4]{0.6} $$ 7. **Calculate the fourth root:** $$ b \approx 0.6^{0.25} \approx 0.8801 $$ **Final answer:** The decay factor is approximately **0.8801** per hour.