How to Calculate Antibiotic Amount in Bloodstream after Exponential Decay

What is bloodstream?

What is meant by the term "bloodstream" and how does it relate to the amount of a certain antibiotic in a patient's body?

Answer:

The bloodstream refers to the blood that circulates in a person's or any organism's body. It is essential for transporting oxygen, nutrients, hormones, and waste products throughout the body.

In the context of the given problem, the bloodstream plays a crucial role in carrying the antibiotic that has been administered to the patient. The antibiotic enters the bloodstream and circulates throughout the body to reach various tissues and organs where it exerts its effect.

Now, let's delve into the specific scenario provided in the question. The problem states that the amount of a certain antibiotic in the bloodstream exhibits exponential decay with a percent decrease of 2% per hour. If the initial dosage is 400 mg, we need to calculate the amount of the antibiotic remaining in the bloodstream after 3 hours.

To solve this problem, we can use the exponential decay formula:

Remaining Amount = Initial Amount * (1 - Rate of Decay)^Time

Plugging in the values given:

Remaining Amount = 400 * (1 - 0.02)^3

Remaining Amount = 400 * (0.98)^3

Remaining Amount ≈ 400 * 0.941192 ≈ 376 mg

Therefore, after 3 hours, approximately 376 milligrams of the antibiotic would be in the patient's bloodstream. This value is the result of the exponential decay process that the antibiotic undergoes.