Current Attempt in Progress The Tojolobal Mayan Indian community in Southern Mexico has available a fixed amount of land.¹ The proportion, P, of land in use for farming t years after 1935 is modeled with the logistic function P = 1+ 3e-0.0275t (a) What proportion of the land was in use for farming in 1935? Enter an exact answer. 1 % of the land was in use in 1935. (b) What is the long-run prediction for this model? Enter an exact answer. In the long-run, P approaches i CO
Current Attempt in Progress The Tojolobal Mayan Indian community in Southern Mexico has available a fixed amount of land.¹ The proportion, P, of land in use for farming t years after 1935 is modeled with the logistic function P = 1+ 3e-0.0275t (a) What proportion of the land was in use for farming in 1935? Enter an exact answer. 1 % of the land was in use in 1935. (b) What is the long-run prediction for this model? Enter an exact answer. In the long-run, P approaches i CO
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Current Attempt in Progress**
The Tojobal Mayan Indian community in Southern Mexico has available a fixed amount of land. The proportion, \( P \), of land in use for farming \( t \) years after 1935 is modeled with the logistic function:
\[ P = \frac{1}{1 + 3e^{-0.07t}} \]
### Questions:
**(a)** What proportion of the land was in use for farming in 1935?
- Enter an exact answer: \(\_\_\_\_\_\_\_\_\_\)
**(b)** What is the long-run prediction for this model?
- Enter an exact answer: \(\_\_\_\_\_\_\_\_\_\%\) of the land was in use in 1935.
**(c)** When was half the land in use for farming?
- In the long-run, \( P \) approaches \(\_\_\_\_\_\_\_\_\_\).
- Round your answer to the nearest year: \(\_\_\_\_\_\_\_\_\_\).
**Note:**
- The problem uses a logistic function to model the proportion of land in use over time.
- The function describes growth that starts slowly, increases rapidly, and then levels off.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb02c27fa-9cde-4c70-877a-bf210a9f7871%2Fe205d023-0e17-4dc3-8676-16ff85735437%2F5uykxk6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Current Attempt in Progress**
The Tojobal Mayan Indian community in Southern Mexico has available a fixed amount of land. The proportion, \( P \), of land in use for farming \( t \) years after 1935 is modeled with the logistic function:
\[ P = \frac{1}{1 + 3e^{-0.07t}} \]
### Questions:
**(a)** What proportion of the land was in use for farming in 1935?
- Enter an exact answer: \(\_\_\_\_\_\_\_\_\_\)
**(b)** What is the long-run prediction for this model?
- Enter an exact answer: \(\_\_\_\_\_\_\_\_\_\%\) of the land was in use in 1935.
**(c)** When was half the land in use for farming?
- In the long-run, \( P \) approaches \(\_\_\_\_\_\_\_\_\_\).
- Round your answer to the nearest year: \(\_\_\_\_\_\_\_\_\_\).
**Note:**
- The problem uses a logistic function to model the proportion of land in use over time.
- The function describes growth that starts slowly, increases rapidly, and then levels off.
![**Educational Website Content: Understanding Land Use Trends**
This section provides an analysis of evolving land use, focusing on the transition of land allocated for farming. The questions and diagrams below are designed to facilitate a deep understanding of the dynamics at play.
---
**Questions and Analysis:**
1. **Long-Run Predictions:**
- **(b) What is the long-run prediction for this model?**
In the long run, \( P \) approaches [Enter an exact answer here].
2. **Historical Land Use Analysis:**
- **(c) When was half the land in use for farming?**
Half the land was in use for farming in approximately [Round your answer to the nearest year].
3. **Rapid Increase in Farming Land:**
- **(d) When is the proportion of land used for farming increasing most rapidly?**
The proportion of land used for farming increases most rapidly in about [Round your answer to the nearest year].
---
**Reference:**
This content is adapted from scholarly work by J. S. Thomas and M. C. Robbins, detailed in "The Limits to Growth in a Tojolobal Maya Ejido," published in Geoscience and Man, 26, pp. 9-16 (Baton Rouge, Geoscience Publications, 1988).
*Note: Diagrams or graphical models accompanying this text would illustrate trends in the proportion of land use over time, emphasizing key years of transition and growth.*
For educators and students, this exercise is crafted to enhance comprehension of statistical models and real-world applications in environmental science.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb02c27fa-9cde-4c70-877a-bf210a9f7871%2Fe205d023-0e17-4dc3-8676-16ff85735437%2F7jqwsmq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content: Understanding Land Use Trends**
This section provides an analysis of evolving land use, focusing on the transition of land allocated for farming. The questions and diagrams below are designed to facilitate a deep understanding of the dynamics at play.
---
**Questions and Analysis:**
1. **Long-Run Predictions:**
- **(b) What is the long-run prediction for this model?**
In the long run, \( P \) approaches [Enter an exact answer here].
2. **Historical Land Use Analysis:**
- **(c) When was half the land in use for farming?**
Half the land was in use for farming in approximately [Round your answer to the nearest year].
3. **Rapid Increase in Farming Land:**
- **(d) When is the proportion of land used for farming increasing most rapidly?**
The proportion of land used for farming increases most rapidly in about [Round your answer to the nearest year].
---
**Reference:**
This content is adapted from scholarly work by J. S. Thomas and M. C. Robbins, detailed in "The Limits to Growth in a Tojolobal Maya Ejido," published in Geoscience and Man, 26, pp. 9-16 (Baton Rouge, Geoscience Publications, 1988).
*Note: Diagrams or graphical models accompanying this text would illustrate trends in the proportion of land use over time, emphasizing key years of transition and growth.*
For educators and students, this exercise is crafted to enhance comprehension of statistical models and real-world applications in environmental science.
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