Solving Digitoxin Rate of Elimination with Geometric Progression

[lionely]

Homework Statement

Patients with certain heart problems are often treated with digitoxin, a derivative of the digitalis plant. The rate at which a person's body eliminates digitoxin is proportional to the amount present. In 1 day, about 10% of any given amount of the drug will be eliminated. Suppose that a "maintenance dose" of 0.05mg is given daily to a patient. Estimate the total amount of digitoxin that should be present in the patient after several months.

Homework Equations

The Attempt at a Solution

My teacher says there is no answer and that there is a problem with the question. But I don't agree!
Several months compared to 1 day is a lot of time, so I believe the answer is the sum to infinity ,
where

the common ratio r, = 0.90 and a =.05

Also when I write out the terms I noticed that each term is equivalent to the GP sum formula.
Meaning T2 = Sum of first two terms of the sequence if it was a GP.

So I believe T∞ = S∞

S∞ = a/(1-r) = .05/(1-.90 ) = .50mg

 

[Dick]

Homework Statement

Patients with certain heart problems are often treated with digitoxin, a derivative of the digitalis plant. The rate at which a person's body eliminates digitoxin is proportional to the amount present. In 1 day, about 10% of any given amount of the drug will be eliminated. Suppose that a "maintenance dose" of 0.05mg is given daily to a patient. Estimate the total amount of digitoxin that should be present in the patient after several months.

Homework Equations

The Attempt at a Solution

My teacher says there is no answer and that there is a problem with the question. But I don't agree!
Several months compared to 1 day is a lot of time, so I believe the answer is the sum to infinity ,
where

the common ratio r, = 0.90 and a =.05

Also when I write out the terms I noticed that each term is equivalent to the GP sum formula.
Meaning T2 = Sum of first two terms of the sequence if it was a GP.

So I believe T∞ = S∞

S∞ = a/(1-r) = .05/(1-.90 ) = .50mg

That's a pretty good estimate, but a more exact answer depends on when in the day the patient takes the maintenance dose and when in the day you measure it. What was your assumption? That ambiguity may be what your teacher is talking about.

 

[lionely]

The assumption I made was that it the series is geometric. I guess and that when they ask me about months I consider that a LONG time compared to a day. So hence the SUm to infinity.