LESSON 9 A quantitative look at the fish population Now you'll study the same fish population as in Lesson 8, but this time you'll answer some quantitative questions. Recall that the fish population, p(t), satisfies the DE p' = p - 0.2p² - 0.7, (fishpop) where p is measured in thousands of kilograms and t is in weeks. The above DE has two equilibrium populations, p₁=0.8 and p₂ = 4.2, both of which are constant solutions of the equation. Since they're solutions, no other solution can cross through them; this can be seen by applying the Existence and Uniqueness Theorem (see your text) to the problem. Thus, the other solutions either approach them asymptotically as t-, or move away from them. Your phase line plot from the last lesson should show this. Task 1. Use the Euler approximation method with a reasonable step size to answer the following questions. 1. If p(0) = 6 (i.e., 6,000 kg), what is the population after 10 weeks? 2. How close is this to the equilibrium point it's approaching? 3. At about what time does the population stop dropping by 100 kg per week? 4. When does the population come within 50 kg of equilibrium?

LESSON 9 A quantitative look at the fish population Now you'll study the same fish population as in Lesson 8, but this time you'll answer some quantitative questions. Recall that the fish population, p(t), satisfies the DE p' = p - 0.2p² - 0.7, (fishpop) where p is measured in thousands of kilograms and t is in weeks. The above DE has two equilibrium populations, p₁=0.8 and p₂ = 4.2, both of which are constant solutions of the equation. Since they're solutions, no other solution can cross through them; this can be seen by applying the Existence and Uniqueness Theorem (see your text) to the problem. Thus, the other solutions either approach them asymptotically as t-, or move away from them. Your phase line plot from the last lesson should show this. Task 1. Use the Euler approximation method with a reasonable step size to answer the following questions. 1. If p(0) = 6 (i.e., 6,000 kg), what is the population after 10 weeks? 2. How close is this to the equilibrium point it's approaching? 3. At about what time does the population stop dropping by 100 kg per week? 4. When does the population come within 50 kg of equilibrium?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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