# Solving Digitoxin Rate of Elimination with Geometric Progression

• lionely
In summary, the rate at which a person's body eliminates digitoxin is proportional to the amount present, with about 10% being eliminated in 1 day. A "maintenance dose" of 0.05mg is given daily to a patient with certain heart problems. Assuming the series is geometric, the sum to infinity can be used to estimate the total amount of digitoxin present after several months. This equals to 0.50mg, but may vary depending on the exact timing of the maintenance dose and measurement. There may be ambiguity in the question, leading to disagreement with the teacher's statement that there is no answer.
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.

## 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

lionely said:

## 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.

## 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.

Last edited:
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.

## 1. What is digitoxin and why is it important to study its rate of elimination?

Digitoxin is a medication used to treat heart conditions, specifically heart failure and atrial fibrillation. It is important to study its rate of elimination because it helps determine the appropriate dosage and frequency of administration for optimal effectiveness and safety.

## 2. What is geometric progression and how does it relate to solving digitoxin rate of elimination?

Geometric progression is a sequence of numbers where each term is obtained by multiplying the previous term by a constant ratio. It relates to solving digitoxin rate of elimination because the drug's concentration in the body decreases exponentially over time, which can be represented by a geometric progression equation.

## 3. How is the rate of elimination of digitoxin measured?

The rate of elimination of digitoxin is measured by determining the half-life of the drug. This is the amount of time it takes for the drug's concentration in the body to decrease by half. The half-life can be calculated by using the drug's elimination rate constant, which can be determined through various methods such as blood or urine tests.

## 4. What factors can affect the rate of elimination of digitoxin?

Several factors can affect the rate of elimination of digitoxin, including age, kidney or liver function, other medications being taken, and overall health status. These factors can alter the drug's elimination rate constant and therefore impact the rate at which it is eliminated from the body.

## 5. How can understanding the geometric progression of digitoxin elimination help in clinical settings?

Understanding the geometric progression of digitoxin elimination can help in clinical settings by guiding healthcare professionals in determining the appropriate dosage and frequency of administration for a patient. By knowing the rate of elimination, they can ensure that the drug remains at a therapeutic level in the body and prevent potential side effects or under/overdosing.

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