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.