### 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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Answered: The rate of change in the number of…

Calculus: Early Transcendentals

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Chapter1: Functions And Models

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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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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 ||