A medication has a half-life of 4 hours after it enters the bloodstream. A nurse administers a dose of 500 milligrams to a patient at noon.

Find the amount of medication, in milligrams (mg), remaining in the patient's body at: (Round to the nearest 10th)
3 p.m. on the same day
8 p.m. on the same day
The expression LaTeX: 500 \cdot \left(\frac12\right)^{\frac54}500 ⋅ ( 1 2 ) 5 4 represents the amount of medicine in the body some time after it is administered. What is that time? (Make sure to signify am or pm)