Biologists are modelling the population of an endangered species of fish in a river system. The indigenous population of the area are permitted to harvest 200 fish once a year in January as part of their culture. Data collected on a recent field trip in December indicate that there are 500 fish in the river system. The data also suggest that the following mathematical model should be used, dy = -2 + y (16 – y), %D dt where y is the population of fish in the river measured in hundreds at time t years after the next harvest. a The term y (16 – y) on the right-hand side represents the familiar logistic growth model. What is the significance of the -2 in this equation? dy b Show that the DE can be re-written as dt :-(y - 4) (y – 12), and write down the initial condition assuming that the harvest goes ahead. 24 3 3 C Show that (у — 4) (у 12) y - 12 4 -
Biologists are modelling the population of an endangered species of fish in a river system. The indigenous population of the area are permitted to harvest 200 fish once a year in January as part of their culture. Data collected on a recent field trip in December indicate that there are 500 fish in the river system. The data also suggest that the following mathematical model should be used, dy = -2 + y (16 – y), %D dt where y is the population of fish in the river measured in hundreds at time t years after the next harvest. a The term y (16 – y) on the right-hand side represents the familiar logistic growth model. What is the significance of the -2 in this equation? dy b Show that the DE can be re-written as dt :-(y - 4) (y – 12), and write down the initial condition assuming that the harvest goes ahead. 24 3 3 C Show that (у — 4) (у 12) y - 12 4 -
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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