Question

When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient's bloodstream after $t$ hours is modeled by $D(t)=50 e^{-0.2 t}$ How many milligrams of the drug remain in the patient's bloodstream after 3 hours?

Name: Problem 23, Chapter 4: College Algebra
Uploaded: 2020-07-27T21:57:37-08:00
Duration: 57 s
Channel: Ankit Gupta
Description: When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient's bloodstream after t hours is modeled by D(t)=50 e^-0.2 t How many milligrams of the drug remain in the patient's bloodstream after 3 hours?

   When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient's bloodstream after $t$ hours is modeled by $D(t)=50 e^{-0.2 t}$ How many milligrams of the drug remain in the patient's bloodstream after 3 hours?

College Algebra

James Stewart,… 7th Edition

Chapter 4, Problem 23

Instant Answer

Solved by Expert Ankit Gupta

07/27/2020

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2 t}$. This function models the amount of drug remaining in the patient's bloodstream after $t$ hours. Show more…

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When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient's bloodstream after $t$ hours is modeled by $D(t)=50 e^{-0.2 t}$ How many milligrams of the drug remain in the patient's bloodstream after 3 hours?

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Key Concepts

Exponential Decay

Exponential decay refers to the process by which a quantity decreases at a rate proportional to its current value. It is used to model various phenomena such as drug concentration reduction in the bloodstream, radioactive decay, and cooling, where the rate of decrease is consistent over time.

Natural Exponential Function

The natural exponential function, denoted by e^x, is fundamental in modeling continuous growth or decay processes. It leverages the mathematical constant e, approximately 2.71828, and is used to accurately represent changes that occur continuously rather than discretely.

Function Evaluation

Function evaluation involves substituting a specific value into the mathematical formula to compute the corresponding output. This process is crucial in applying abstract models, such as the one for drug decay, to obtain concrete numerical predictions for given conditions.

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