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A year after Lake Nittany was stocked with 1000 rainbow trout, the population grew by 15%. Previ- ous attempts at seeding Lake Nittany with trout indicate that the lake should be capable of supporting 15000 trout. Set up and solve a logistic differential equation of the form dP dt = kP(M - P) to find P(t), the population of trout at time t. When will the lake will have 85% of its capacity of 15000 trout?

A year after Lake Nittany was stocked with 1000 rainbow trout, the population grew by 15%. Previ- ous attempts at seeding Lake Nittany with trout indicate that the lake should be capable of supporting 15000 trout. Set up and solve a logistic differential equation of the form dP dt = kP(M - P) to find P(t), the population of trout at time t. When will the lake will have 85% of its capacity of 15000 trout?

Calculus: Early Transcendentals
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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A year after Lake Nittany was stocked with 1000 rainbow trout, the population grew by 15%. Previ- ous attempts at seeding Lake Nittany with trout indicate that the lake should be capable of supporting 15000 trout. Set up and solve a logistic differential equation of the form dP dt = kP(M – P) to find P(t), the population of trout at time t. When will the lake will have 85% of its capacity of 15000 trout?
Transcribed Image Text:A year after Lake Nittany was stocked with 1000 rainbow trout, the population grew by 15%. Previ- ous attempts at seeding Lake Nittany with trout indicate that the lake should be capable of supporting 15000 trout. Set up and solve a logistic differential equation of the form dP dt = kP(M – P) to find P(t), the population of trout at time t. When will the lake will have 85% of its capacity of 15000 trout?
Expert Solution
Step 1: Introduce to the given information

A logistic differential equation is of the form,

fraction numerator d P over denominator d t end fraction space equals space k P left parenthesis space M space minus space P space right parenthesis space

After a year, the population is 1000 rainbow trout.

The population grew by 15%.

Maximum population the lake should be capable of supporting = 15000 trout


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