Math Problem Statement

The concentration of a drug in a patient's bloodstream is modeled by A(t) = 377e^(-0.121t) units. Find the concentration after 2 hours.

Solution

It seems like you've uploaded an image of a question related to a medication or solution concentration. Since I can't directly interact with the image itself, I will transcribe and help solve the problem based on what I can see. Here’s what I gather from the image:


Problem: You are given a concentration value of a drug in A(t) = 377e^(-0.121t), where the drug concentration decreases exponentially over time.

The task is to find the concentration when t = 2 hours.

Steps:

  1. Plug the value of t=2t = 2 into the equation A(t)=377e0.121tA(t) = 377e^{-0.121t}.

    A(2)=377e0.121(2)A(2) = 377e^{-0.121(2)}

  2. Perform the calculation.

I will calculate this for you right now.The concentration of the drug after 2 hours is approximately 295.97 (rounded to two decimal places).

Let me know if you want further details or explanations.

Here are some related questions to expand your understanding:

  1. What is the significance of the rate constant (-0.121) in this problem?
  2. How would the concentration change if the rate constant were smaller or larger?
  3. Can you explain how exponential decay models are used in other real-life situations?
  4. How would you find the time at which the concentration falls below a certain threshold, like 100 units?
  5. What role does the initial concentration (377) play in determining future concentrations?

Tip: Exponential decay functions are commonly used to model processes where something decreases at a rate proportional to its current value, such as radioactive decay or cooling processes.

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Math Problem Analysis

Mathematical Concepts

Exponential decay
Algebra
Exponential functions

Formulas

Exponential decay formula: A(t) = A0 * e^(-kt)

Theorems

Properties of exponential functions

Suitable Grade Level

Grades 10-12