The Recommended Dosage Of Ibuprofen For An Adult Is 400 Mg. Each Hour, The Amount Of Ibuprofen In The Person's System Decreases By About 29.5%.Which Function Models The Amount Of Ibuprofen Left In Your System After $x$ Hours?A. $a(x) =

The Recommended Dosage of Ibuprofen and Its Exponential Decay

Understanding the Problem

When taking ibuprofen, it's essential to know how the medication is absorbed and eliminated by the body. The recommended dosage of ibuprofen for an adult is 400 mg. However, the amount of ibuprofen in the person's system decreases over time due to various factors such as metabolism and excretion. In this article, we will explore the concept of exponential decay and how it can be used to model the amount of ibuprofen left in the system after a certain period.

Exponential Decay

Exponential decay is a process where the amount of a substance decreases over time at a rate proportional to its current amount. This type of decay is often modeled using the exponential function, which has the general form:

$$y = ab^x$$

where $y$ is the amount of the substance at time $x$, $a$ is the initial amount, and $b$ is the decay rate.

Modeling the Amount of Ibuprofen Left in the System

In this problem, we are given that the amount of ibuprofen in the person's system decreases by about 29.5% every hour. This means that the decay rate is 29.5% or 0.295 as a decimal. We can use this information to model the amount of ibuprofen left in the system after $x$ hours.

Let $y$ be the amount of ibuprofen left in the system after $x$ hours. We know that the initial amount of ibuprofen is 400 mg, so $a = 400$. We also know that the decay rate is 0.295, so $b = 1 - 0.295 = 0.705$.

Using the exponential function, we can model the amount of ibuprofen left in the system as follows:

$$y = 400(0.705)^x$$

This function represents the amount of ibuprofen left in the system after $x$ hours.

Solving for the Amount of Ibuprofen Left in the System

To find the amount of ibuprofen left in the system after a certain period, we can plug in the value of $x$ into the function. For example, to find the amount of ibuprofen left in the system after 2 hours, we can plug in $x = 2$:

$$y = 400(0.705)^2$$

Using a calculator, we can evaluate this expression to find the amount of ibuprofen left in the system after 2 hours:

$$y = 400(0.705)^2 = 157.41$$

Therefore, after 2 hours, there will be approximately 157.41 mg of ibuprofen left in the system.

Graphing the Function

To visualize the amount of ibuprofen left in the system over time, we can graph the function $y = 400(0.705)^x$. This graph will show the amount of ibuprofen left in the system at different times.

Using a graphing calculator or software, we can create a graph of the function. The graph will show that the amount of ibuprofen left in the system decreases exponentially over time.

Conclusion

In this article, we explored the concept of exponential decay and how it can be used to model the amount of ibuprofen left in the system after a certain period. We used the exponential function to model the amount of ibuprofen left in the system and solved for the amount of ibuprofen left in the system after 2 hours. We also graphed the function to visualize the amount of ibuprofen left in the system over time.

References

• [1] "Ibuprofen: MedlinePlus Drug Information." National Library of Medicine, 2022.
• [2] "Exponential Decay." Math Is Fun, 2022.
• [3] "Graphing Exponential Functions." Mathway, 2022.

Frequently Asked Questions

• Q: What is the recommended dosage of ibuprofen for an adult? A: The recommended dosage of ibuprofen for an adult is 400 mg.
• Q: How does the amount of ibuprofen in the person's system decrease over time? A: The amount of ibuprofen in the person's system decreases by about 29.5% every hour.
• Q: How can we model the amount of ibuprofen left in the system after a certain period? A: We can use the exponential function to model the amount of ibuprofen left in the system.

Additional Resources

• [1] "Ibuprofen: Side Effects, Dosage, and Interactions." Healthline, 2022.
• [2] "Exponential Decay: A Tutorial." Khan Academy, 2022.
• [3] "Graphing Exponential Functions: A Guide." Math Open Reference, 2022.
  The Recommended Dosage of Ibuprofen and Its Exponential Decay: Q&A

Understanding the Problem

When taking ibuprofen, it's essential to know how the medication is absorbed and eliminated by the body. The recommended dosage of ibuprofen for an adult is 400 mg. However, the amount of ibuprofen in the person's system decreases over time due to various factors such as metabolism and excretion. In this article, we will explore the concept of exponential decay and how it can be used to model the amount of ibuprofen left in the system after a certain period.

Q&A

Q: What is the recommended dosage of ibuprofen for an adult? A: The recommended dosage of ibuprofen for an adult is 400 mg.

Q: How does the amount of ibuprofen in the person's system decrease over time? A: The amount of ibuprofen in the person's system decreases by about 29.5% every hour.

Q: How can we model the amount of ibuprofen left in the system after a certain period? A: We can use the exponential function to model the amount of ibuprofen left in the system.

Q: What is the formula for the exponential function that models the amount of ibuprofen left in the system? A: The formula for the exponential function is:

$$y = 400(0.705)^x$$

Q: How can we use the exponential function to find the amount of ibuprofen left in the system after a certain period? A: We can plug in the value of $x$ into the function to find the amount of ibuprofen left in the system after a certain period.

Q: What is the amount of ibuprofen left in the system after 2 hours? A: To find the amount of ibuprofen left in the system after 2 hours, we can plug in $x = 2$ into the function:

$$y = 400(0.705)^2 = 157.41$$

Therefore, after 2 hours, there will be approximately 157.41 mg of ibuprofen left in the system.

Q: How can we graph the function to visualize the amount of ibuprofen left in the system over time? A: We can use a graphing calculator or software to create a graph of the function.

Q: What does the graph of the function show? A: The graph of the function shows that the amount of ibuprofen left in the system decreases exponentially over time.

Q: What are some real-world applications of exponential decay? A: Exponential decay has many real-world applications, including modeling population growth and decline, radioactive decay, and the spread of diseases.

Q: How can we use exponential decay to model the spread of diseases? A: We can use exponential decay to model the spread of diseases by assuming that the number of infected individuals decreases exponentially over time.

Q: What are some limitations of using exponential decay to model the spread of diseases? A: One limitation of using exponential decay to model the spread of diseases is that it assumes that the rate of infection is constant over time, which may not be the case in reality.

Conclusion

In this article, we explored the concept of exponential decay and how it can be used to model the amount of ibuprofen left in the system after a certain period. We used the exponential function to model the amount of ibuprofen left in the system and solved for the amount of ibuprofen left in the system after 2 hours. We also graphed the function to visualize the amount of ibuprofen left in the system over time.

References

• [1] "Ibuprofen: MedlinePlus Drug Information." National Library of Medicine, 2022.
• [2] "Exponential Decay." Math Is Fun, 2022.
• [3] "Graphing Exponential Functions." Mathway, 2022.

Frequently Asked Questions

• Q: What is the recommended dosage of ibuprofen for an adult? A: The recommended dosage of ibuprofen for an adult is 400 mg.
• Q: How does the amount of ibuprofen in the person's system decrease over time? A: The amount of ibuprofen in the person's system decreases by about 29.5% every hour.
• Q: How can we model the amount of ibuprofen left in the system after a certain period? A: We can use the exponential function to model the amount of ibuprofen left in the system.

Additional Resources

• [1] "Ibuprofen: Side Effects, Dosage, and Interactions." Healthline, 2022.
• [2] "Exponential Decay: A Tutorial." Khan Academy, 2022.
• [3] "Graphing Exponential Functions: A Guide." Math Open Reference, 2022.