**Problem 7:** In an effort to enhance a fishery, 100 trout were initially put in a small lake. Fishery Department biologists predict that the rate of growth of the trout population is modeled by the logistic differential equation: \[ \frac{dP}{dt} = 0.1P \left( 1 - \frac{P}{600} \right) \] where time \(t\) is measured in months. I. The growth rate of the fish population is greatest at \(P = 600\). II. If \(P > 600\), the population of fish is decreasing. III. \(\lim_{{t \to \infty}} P(t) = 600\) **Options:** - (A) I only - (B) II only - (C) I and III only - (D) II and III only - (E) I, II, and III
**Problem 7:** In an effort to enhance a fishery, 100 trout were initially put in a small lake. Fishery Department biologists predict that the rate of growth of the trout population is modeled by the logistic differential equation: \[ \frac{dP}{dt} = 0.1P \left( 1 - \frac{P}{600} \right) \] where time \(t\) is measured in months. I. The growth rate of the fish population is greatest at \(P = 600\). II. If \(P > 600\), the population of fish is decreasing. III. \(\lim_{{t \to \infty}} P(t) = 600\) **Options:** - (A) I only - (B) II only - (C) I and III only - (D) II and III only - (E) I, II, and III
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**Problem 7:**
In an effort to enhance a fishery, 100 trout were initially put in a small lake. Fishery Department biologists predict that the rate of growth of the trout population is modeled by the logistic differential equation:
\[
\frac{dP}{dt} = 0.1P \left( 1 - \frac{P}{600} \right)
\]
where time \(t\) is measured in months.
I. The growth rate of the fish population is greatest at \(P = 600\).
II. If \(P > 600\), the population of fish is decreasing.
III. \(\lim_{{t \to \infty}} P(t) = 600\)
**Options:**
- (A) I only
- (B) II only
- (C) I and III only
- (D) II and III only
- (E) I, II, and III](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31f979b8-8825-4064-8795-d73ff3ae8525%2F6b7cedad-69da-4c5d-b777-abd18982b563%2Fvz7ol9k.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 7:**
In an effort to enhance a fishery, 100 trout were initially put in a small lake. Fishery Department biologists predict that the rate of growth of the trout population is modeled by the logistic differential equation:
\[
\frac{dP}{dt} = 0.1P \left( 1 - \frac{P}{600} \right)
\]
where time \(t\) is measured in months.
I. The growth rate of the fish population is greatest at \(P = 600\).
II. If \(P > 600\), the population of fish is decreasing.
III. \(\lim_{{t \to \infty}} P(t) = 600\)
**Options:**
- (A) I only
- (B) II only
- (C) I and III only
- (D) II and III only
- (E) I, II, and III
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