Q4.4 For a certain decision, the time it takes to respond is a logarithmic function of the number of the choices faced. One model is R = .17+ .44 log (N), where R is the reaction time in seconds and N is the number of choices. (a) Find the average rate of change of the reaction time when the number of choices goes from 10 to 100. (b) Find the rate of change of the reaction time with respect to the number of choices.
Q4.4 For a certain decision, the time it takes to respond is a logarithmic function of the number of the choices faced. One model is R = .17+ .44 log (N), where R is the reaction time in seconds and N is the number of choices. (a) Find the average rate of change of the reaction time when the number of choices goes from 10 to 100. (b) Find the rate of change of the reaction time with respect to the number of choices.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.4: Definition Of The Derivative
Problem 49E
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Please solve only 4.4
![On this educational page, we explore various mathematical models and their applications, including reaction to medication, decision-making time, and solving limits. Here, we delve into model analysis and calculation techniques step by step.
**Q4.3**
**Modeling the Human Body's Reaction to Dosage**
The human body's reaction to a dose of medicine can be represented by the function:
\[ F = \frac{1}{3}(KM^2 - M^3) \]
where \( K \) is a positive constant and \( M \) is the amount of medicine absorbed into the bloodstream. The derivative, represented by \( S = \frac{dF}{dM} \), serves as a measure of the body's sensitivity to the medicine.
**Task:** Find the sensitivity \( S \).
**Q4.4**
**Reaction Time in Decision-Making**
For a certain decision, the response time is modeled as a logarithmic function of the number of choices faced. The model is given by:
\[ R = 0.17 + 0.44 \log(N) \]
where \( R \) is the reaction time in seconds, and \( N \) is the number of choices.
**Tasks:**
- **(a):** Calculate the average rate of change in reaction time when the number of choices increases from 10 to 100.
- **(b):** Determine the rate of change of the reaction time with respect to the number of choices.
**Q5**
**Solving Limits**
Evaluate the following limit:
\[ \lim_{x \to \infty} \frac{\sinh(x)}{e^x} \]
In the provided problems, students will apply calculus techniques such as differentiation and limit evaluation to derive insights and solutions for practical models.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2cc04b1e-803c-4d9d-b550-d2ae04bcc2b3%2F4a8f9423-df04-42ad-b4ec-dd3d1f3a6778%2Fl54m5s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:On this educational page, we explore various mathematical models and their applications, including reaction to medication, decision-making time, and solving limits. Here, we delve into model analysis and calculation techniques step by step.
**Q4.3**
**Modeling the Human Body's Reaction to Dosage**
The human body's reaction to a dose of medicine can be represented by the function:
\[ F = \frac{1}{3}(KM^2 - M^3) \]
where \( K \) is a positive constant and \( M \) is the amount of medicine absorbed into the bloodstream. The derivative, represented by \( S = \frac{dF}{dM} \), serves as a measure of the body's sensitivity to the medicine.
**Task:** Find the sensitivity \( S \).
**Q4.4**
**Reaction Time in Decision-Making**
For a certain decision, the response time is modeled as a logarithmic function of the number of choices faced. The model is given by:
\[ R = 0.17 + 0.44 \log(N) \]
where \( R \) is the reaction time in seconds, and \( N \) is the number of choices.
**Tasks:**
- **(a):** Calculate the average rate of change in reaction time when the number of choices increases from 10 to 100.
- **(b):** Determine the rate of change of the reaction time with respect to the number of choices.
**Q5**
**Solving Limits**
Evaluate the following limit:
\[ \lim_{x \to \infty} \frac{\sinh(x)}{e^x} \]
In the provided problems, students will apply calculus techniques such as differentiation and limit evaluation to derive insights and solutions for practical models.
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