The rate of change in the number of deer, D, within a town is inversely proportional to the number of people, p, living within the town Write the differential equation to solve for D(t). Do not solve. dD O O | | | | O || O k D = pk = Dk k P dD ||
The rate of change in the number of deer, D, within a town is inversely proportional to the number of people, p, living within the town Write the differential equation to solve for D(t). Do not solve. dD O O | | | | O || O k D = pk = Dk k P dD ||
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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![### Differential Equations - Deer Population Dynamics
**Problem Statement:**
The rate of change in the number of deer, \( D \), within a town is inversely proportional to the number of people, \( p \), living within the town.
Write the differential equation to solve for \( D(t) \).
**Note:** Do not solve the differential equation.
**Options:**
- \(\frac{dD}{dp} = \frac{k}{D}\)
- \(\frac{dD}{dp} = pk\)
- \(\frac{dD}{dp} = Dk\)
- \(\frac{dD}{dp} = \frac{k}{p}\) \( \leftarrow \text{Correct option is highlighted}\)
### Explanation:
The rate of change in the number of deer \( D \) is given as inversely proportional to the number of people \( p \). This relationship is mathematically expressed as:
\[
\frac{dD}{dp} = \frac{k}{p}
\]
Where \( k \) is a constant of proportionality. This means that as the number of people \( p \) increases, the rate of change in the number of deer decreases proportionally.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf75a45c-687d-4994-8001-f519eebb3c9c%2Fcfec701f-1181-4d91-976e-66b5ad421900%2Fry7dagl_processed.png&w=3840&q=75)
Transcribed Image Text:### Differential Equations - Deer Population Dynamics
**Problem Statement:**
The rate of change in the number of deer, \( D \), within a town is inversely proportional to the number of people, \( p \), living within the town.
Write the differential equation to solve for \( D(t) \).
**Note:** Do not solve the differential equation.
**Options:**
- \(\frac{dD}{dp} = \frac{k}{D}\)
- \(\frac{dD}{dp} = pk\)
- \(\frac{dD}{dp} = Dk\)
- \(\frac{dD}{dp} = \frac{k}{p}\) \( \leftarrow \text{Correct option is highlighted}\)
### Explanation:
The rate of change in the number of deer \( D \) is given as inversely proportional to the number of people \( p \). This relationship is mathematically expressed as:
\[
\frac{dD}{dp} = \frac{k}{p}
\]
Where \( k \) is a constant of proportionality. This means that as the number of people \( p \) increases, the rate of change in the number of deer decreases proportionally.
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