Question 930634
We should give that patient the next dose when the level in his bloodstream is 1.5mg/mL.
The blood level will be be reduced to 1.5mg/mL = (1/2)(3mg/mL)
in 1 half-life = 75 minutes = 1 hour + 15 minutes, at 3:15PM.
At that point, we should give a dose large enough to raise his blood level back to 3mg/mL.
That requires a rise in blood concentration of 3mg/mL - 1.5mg/mL = 1.5mg/mL,
and we can assume that a blood level rise of 1.5mg/mL = (1/2)(3mg/mL) requires
1/2 of the original dose that caused a rise of 3mg/mL.
So the next dose will be 1/2 or 50% of the initial dose.


NOTE:
You may be thinking of formulas from the textbook.
They are not needed on this case, and memorizing them is not needed either.
{{{A/A[0]=(1/2)^(t/75)}}} is intuitive and gets you to
{{{ln(A/A[0])=-ln(2)*t/75}}} and to
{{{A/A[0]=e^(-ln(2)*"t/75")}}}