Subjects algebra

Medication Concentration A540C5

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Medication Concentration A540C5


1. **State the problem:** We need to find the concentration $C$ of medication in the bloodstream 4 hours after administration, given by the formula: $$C = 66 \left(e^{-0.5t} - e^{-2t}\right)$$ where $t$ is the time in hours. 2. **Substitute $t=4$ into the formula:** $$C = 66 \left(e^{-0.5 \times 4} - e^{-2 \times 4}\right) = 66 \left(e^{-2} - e^{-8}\right)$$ 3. **Calculate the exponential terms:** - $e^{-2} \approx 0.1353$ - $e^{-8} \approx 0.000335$ 4. **Evaluate the difference:** $$0.1353 - 0.000335 = 0.134965$$ 5. **Multiply by 66:** $$C = 66 \times 0.134965 \approx 8.907$$ **Final answer:** The concentration of the medication 4 hours after administration is approximately $8.91$ milligrams per unit volume.