https://file.aiquickdraw.com/mathbot/file/1726471811500fqais844.jpg

The image presents a problem regarding the concentration of a medication in the bloodstream over time. The given function is:

\[
C(t) = \frac{3t}{t + 6}
\]

Where:
- \(C(t)\) represents the concentration of the medication in the bloodstream at time \(t\) (in hours).
- \(t\) is the time in hours after the medication was taken.

The problem asks to find the concentration when \(t = 4\) hours.

Let's compute the concentration at \(t = 4\):

\[
C(4) = \frac{3 \cdot 4}{4 + 6}
\]

Now I will calculate this.The concentration of the medication in the bloodstream after 4 hours is \( C(4) = 1.2 \).

Would you like more details or explanations on how this was solved? 

Here are 5 related questions you might find useful:
1. How does the concentration change as \( t \) increases further?
2. What happens to the concentration as \( t \to 0 \)?
3. What is the maximum possible concentration of the medication?
4. How would you calculate the time at which the concentration is half of its maximum value?
5. How does changing the function affect the shape of the concentration graph?

**Tip:** When working with rational functions like this, analyzing the behavior as \( t \) approaches very large values or zero can provide insight into long-term trends.

Let C(t) = 3t / (t + 6) be the function that describes the concentration of a certain medication in the bloodstream over time t. If 4 hours have passed after the medicine was intake, how concentrated is it in the blood?

Solve a rational function problem where you determine the concentration of medication in the bloodstream after 4 hours. This example uses substitution in the formula C(t) = 3t / (t + 6) to find the concentration at t = 4. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation