Question

Health/Medicine. During the course of treatment of an illness, the concentration of a dose of a drug (in $\mathrm{mcg} / \mathrm{mL}$ ) in the bloodstream fluctuates according to the model $$ C(t)=60-0.75 t^{2} $$ where $t=0$ is when the drug was administered. Assuming a single dose of the drug is administered, in how many hours (to the nearest hour) after being administered will the drug be climinated from the bloodstream?

Name: Problem 72, Chapter 2: Precalculus
Uploaded: 2020-08-14T08:06:44-08:00
Duration: 2 min 19 s
Channel: Supratim Roy
Description: Health/Medicine. During the course of treatment of an illness, the concentration of a dose of a drug (in mcg / mL ) in the bloodstream fluctuates according to the model C(t)=60-0.75 t^2 where t=0 is when the drug was administered. Assuming a single dose of the drug is administered, in how many hours (to the nearest hour) after being administered will the drug be climinated from the bloodstream?

   Health/Medicine. During the course of treatment of an illness, the concentration of a dose of a drug (in $\mathrm{mcg} / \mathrm{mL}$ ) in the bloodstream fluctuates according to the model
$$ C(t)=60-0.75 t^{2} $$
where $t=0$ is when the drug was administered. Assuming a single dose of the drug is administered, in how many hours (to the nearest hour) after being administered will the drug be climinated from the bloodstream?

Precalculus

Cynthia Young 2nd Edition

Chapter 2, Problem 72

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Solved by Expert Supratim Roy

08/14/2020

Step 1

75 t^{2}$ represents the concentration of a drug in the bloodstream at any time $t$ after the drug was administered. We are asked to find the time at which the drug will be eliminated from the bloodstream. This corresponds to the time at which the concentration of Show more…

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Health/Medicine. During the course of treatment of an illness, the concentration of a dose of a drug (in $\mathrm{mcg} / \mathrm{mL}$ ) in the bloodstream fluctuates according to the model $$ C(t)=60-0.75 t^{2} $$ where $t=0$ is when the drug was administered. Assuming a single dose of the drug is administered, in how many hours (to the nearest hour) after being administered will the drug be climinated from the bloodstream?

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Key Concepts

Pharmacokinetics

Pharmacokinetics is the branch of medicine that studies how a drug is absorbed, distributed, metabolized, and eliminated by the body. It uses mathematical models to track the time course of drug concentrations in biological fluids.

Mathematical Modeling

Mathematical modeling involves creating functions that represent biological processes such as drug concentration over time. These models help in predicting how a drug behaves in the body and in making informed decisions about dosing regimens.

Solving Equations for Elimination Time

Determining when a drug is eliminated from the body often involves solving equations where the drug concentration is set to zero. This process typically uses algebraic methods, such as solving quadratic equations, to find the time at which the elimination threshold is reached.

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