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39. Population of Fish Let f(t) denote the number (in thousands) of fish in a lake after t years, and suppose that f(t) satisfies the differential equation y' = 0.1y (5 - y).

39. Population of Fish Let f(t) denote the number (in thousands) of fish in a lake after t years, and suppose that f(t) satisfies the differential equation y' = 0.1y (5 - y).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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39. Population of Fish Let f(t) denote the number (in thousands) of fish in a lake after t years, and suppose that f(t) satisfies the differential equation y' = 0.1y(5 y). The slope field for this equation is shown in Fig. 9. (a) With the help of the slope field, discuss what happens to an initial population of 6000 fish. Does it increase or decrease? (b) How about an initial population of 1000 fish? Does it in- crease or decrease? (c) On the slope field in Fig. 9 or a copy of it, draw the solu- tion of the initial-value problem What does this solution represent? y (in thousands) 6 5 4 3 2 y' = 0.1y(5-y), y(0) = 1. 1 0 1 Figure 9 2 . ܠܐ 3 4 ·10 5 6 t
Transcribed Image Text:39. Population of Fish Let f(t) denote the number (in thousands) of fish in a lake after t years, and suppose that f(t) satisfies the differential equation y' = 0.1y(5 y). The slope field for this equation is shown in Fig. 9. (a) With the help of the slope field, discuss what happens to an initial population of 6000 fish. Does it increase or decrease? (b) How about an initial population of 1000 fish? Does it in- crease or decrease? (c) On the slope field in Fig. 9 or a copy of it, draw the solu- tion of the initial-value problem What does this solution represent? y (in thousands) 6 5 4 3 2 y' = 0.1y(5-y), y(0) = 1. 1 0 1 Figure 9 2 . ܠܐ 3 4 ·10 5 6 t
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