Question
please also find P3
The figure below shows the quantity of the drug atenolol in the blood as a function of time, with the first dose at time t = 0. Suppose atenolol is taken in 25 mg doses once a day to lower blood pressure. If the half-life of the atenolol in the blood is 6.2 hours, the percentage of atenolol still present at the end of a 24 hours period is approximately 7 %. Find expressions for the quantities Qo, Q1, Q2..., and Qn shown in the figure. Then write the expression for Qn in closed-form. Qo = Q1 = Q2 = ... Qn = Find expressions for the quantities P1, P2, P3..., and Pn shown in the figure. Then write the expression for Pn in closed-form. P1 = P2 =
Explanation / Answer
Q0 = 25 mg
Q1 = 25 + 25*0.07 = 26.75 mg
Q2 = 25 + 26.75*0.07 = 26.8725 mg
Qn = 25 + 0.07*Q(n-1)
P0 = 0.07*25 = 1.75 mg
P1 = 0.07*26.75 = 1.8725 mg
P2 = 0.07 * 26.8725 = 1.881075 mg
Pn = 0.07 * Qn mg
Thus, P3 = 0.07 * Q3 = 0.07 * (25 + 0.07*26.8725) = 1.88167 mg