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I've opened the image, and it seems to contain a problem related to interpreting a function \( f(t) = \frac{750}{40+ t^2} \), which models the amount of medicine in a person's bloodstream over time.

I will transcribe the relevant information from the image to help solve the problem.

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**Problem:**

Given the function \( f(t) = \frac{750}{40 + t^2} \), where \( t \) represents hours after a dose of medicine, the questions ask for specific evaluations and interpretations of \( f(t) \) at various time points, such as \( t = 0 \), \( t = 1 \), and \( t = 2 \).

The task is to:

1. **Evaluate** \( f(t) \) at different values of \( t \).
2. **Interpret** the result in terms of the amount of medicine in the bloodstream at given times.
3. **Justify** which function best models the situation.

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Let's start by evaluating \( f(t) \) at \( t = 0 \), \( t = 1 \), and \( t = 2 \).The evaluations of the function \( f(t) = \frac{750}{40 + t^2} \) at different times are as follows:

- \( f(0) = \frac{75}{4} = 18.75 \) milligrams
- \( f(1) = \frac{750}{41} \approx 18.29 \) milligrams
- \( f(2) = \frac{375}{22} \approx 17.05 \) milligrams

**Interpretation**:
1. \( f(0) \) represents the amount of medicine (18.75 mg) in the bloodstream immediately after the dose.
2. \( f(1) \) represents the amount of medicine (approximately 18.29 mg) one hour after the dose.
3. \( f(2) \) represents the amount of medicine (approximately 17.05 mg) two hours after the dose.

These results indicate a gradual decrease in the amount of medicine over time.

Would you like further details on this, or should I assist with any other part of the question?

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Here are 5 related questions you might find helpful:

1. How does the function \( f(t) \) behave as time increases?
2. How would you calculate the rate of change of medicine concentration over time?
3. What happens to the function \( f(t) \) as \( t \) approaches infinity?
4. How can this model be applied to other biological processes involving decay or absorption?
5. How would modifying the parameters of the function affect the medicine concentration?

**Tip:** Understanding the long-term behavior of the function, like its limit as \( t \to \infty \), can provide insights into how medicine is processed in the body over time.

After taking a dose of medicine, the amount of medicine remaining in a person's bloodstream, in milligrams, after t hours can be modeled by the function f(t) = 750 / (40 + t^2). Interpret the given function values and determine an appropriate function for the situation.

Explore the function f(t) = 750 / (40 + t^2) to model the amount of medicine in a person's bloodstream. This detailed example walks through how to evaluate the function at various times (t = 0, t = 1, t = 2) and interpret the results. Learn how this function shows the gradual decrease in medicine concentration over time, suitable for Grades 10-12.

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