Please answer only 4.3 ### Mathematics in Medicine: Understanding Sensitivity and Reaction Time#### Q4.3 - Sensitivity of the Human Body to MedicineThe human body’s response to a dose of medicine can be modeled by a function of the form:\[ F = \frac{1}{3} (KM^2 - M^3) \]where \( K \) is a positive constant, and \( M \) represents the amount of medicine absorbed in the blood. To determine the sensitivity of the body to the medicine, we consider the derivative:\[ S = \frac{dF}{dM} \]which reflects the rate of change of \( F \) with respect to \( M \). This derivative \( S \) serves as a measure of the sensitivity of the body to the medicine. **Your task** is to find the sensitivity \( S \).#### Q4.4 - Reaction Time in Decision-MakingWhen facing a decision, the time it takes to respond is often a logarithmic function of the number of choices available. This can be modeled by the formula:\[ R = 0.17 + 0.44 \log (N) \]where \( R \) is the reaction time in seconds, and \( N \) is the number of choices.(a) **Average Rate of Change**:Compute the average rate of change of the reaction time when the number of choices ranges from 10 to 100.(b) **Rate of Change with Respect to Number of Choices**:Determine the rate of change of the reaction time with respect to the number of choices.---By understanding these mathematical models, students can appreciate how mathematics applies to real-world scenarios, such as medical responses and decision-making processes. These exercises highlight the importance of differential calculus in analyzing and interpreting such models.

The human body reaction to a dose can be modeled by the function where K is a constant M is the…

Q4.3 The human body's reaction to a dose of medicine can be modeled by a function of the form F = 1 (KM2-M³) where K is a positive constant and M is the amount of medicine absorbed in the 3 dF blood. The derivative S can be thought of as a measure of the sensitivity of the body to the dM medicine. Find the sensitivity S.

Q4.3 The human body's reaction to a dose of medicine can be modeled by a function of the form F = 1 (KM2-M³) where K is a positive constant and M is the amount of medicine absorbed in the 3 dF blood. The derivative S can be thought of as a measure of the sensitivity of the body to the dM medicine. Find the sensitivity S.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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