A team of biologists stocked a lake with 100 fish of one species to conduct an experiment. They concluded that the rate of increase of the fish population is directly proportional to the population at that time, p(t) as well as to the difference between species' carrying capacity and the current population. The carrying capacity for this fish species in the lake was estimated to be 1000. It was observed that the number of the fish tripled in the first year. What would be the fish population in 5 years?

A team of biologists stocked a lake with 100 fish of one species to conduct an experiment. They concluded that the rate of increase of the fish population is directly proportional to the population at that time, p(t) as well as to the difference between species' carrying capacity and the current population. The carrying capacity for this fish species in the lake was estimated to be 1000. It was observed that the number of the fish tripled in the first year. What would be the fish population in 5 years?

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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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

1.
A team of biologists stocked a lake with 100 fish of one species to conduct an experiment. They
concluded that the rate of increase of the fish population is directly proportional to the population at
that time, p(t) as well as to the difference between species' carrying capacity and the current
population. The carrying capacity for this fish species in the lake was estimated to be 1000. It was
observed that the number of the fish tripled in the first year. What would be the fish population in 5
years?

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