9. 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) with the slope field shown below: y (in thousands) 5. 4. 3 6 (a) Determine what happens to an initial population of 6,500 fish. Does it increase or decrease? (b) Determine the numbers in the fish population that they will stay constant over time. (c) If the initial population is 1,000 fish, find the approximate of time when the lake has 4,000 fish in population.

9. 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) with the slope field shown below: y (in thousands) 5. 4. 3 6 (a) Determine what happens to an initial population of 6,500 fish. Does it increase or decrease? (b) Determine the numbers in the fish population that they will stay constant over time. (c) If the initial population is 1,000 fish, find the approximate of time when the lake has 4,000 fish in population.

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

9. 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)
with the slope field shown below:
y (in thousands)
6-
5-
4
3
(a) Determine what happens to an
initial population of 6,500 fish.
Does it increase or decrease?
(b) Determine the numbers in the fish
population that they will stay
constant over time.
(c) If the initial population is 1,000 fish,
find the approximate of time when
the lake has 4,000 fish in
population.

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