Question
A certain drug has a half-life of about 2 hours in blood stream. The drug is formula to be administered in dose of ''D'' milligram every 4 hours. But ''D'' is yet to be determined.
A) Show that the number of milligrams of drug in blood stream after the nth dose has been administered is:
D+(1/4)D+........+D(1/4)^n-1
and that this sum is approx; (4/3)D for large values of "n",?
A) Show that the number of milligrams of drug in blood stream after the nth dose has been administered is:
D+(1/4)D+........+D(1/4)^n-1
and that this sum is approx; (4/3)D for large values of "n",?
Answers
D+(1/4)D+........+D(1/4)^n-1
= D(1 + 1/4 + 1/16 + (1/4)^(n-1) )
= D(geometric series of n terms, with a = 1, r = 1/4)
sum(n) = a/(1-r) , as n ---> ∞
= 1/(1-1/4)
= 1/(3/4)
= 4/3
so the amount = D(4/3)
= D(1 + 1/4 + 1/16 + (1/4)^(n-1) )
= D(geometric series of n terms, with a = 1, r = 1/4)
sum(n) = a/(1-r) , as n ---> ∞
= 1/(1-1/4)
= 1/(3/4)
= 4/3
so the amount = D(4/3)