A biologist noticed that a small forest has a population of deer that naturally grows according to the logistic model y' = 0.0005y(300 – y) where y is the number of deer at time t measured in months. The carrying capacity of this forest is deer. In January 2021, a disease began killing the deer at a rate of 10 deer per month. If there were 110 deer in the pond when the biologist first noticed the disease (at time t = 0)), then the number of deer w and reach in increase the long run. decrease After many months, the biologist finds that the disease is not affecting the deer as much and fewer deer are dying from it each month. The deer population has rebounded and is now at a stable size of 270. Based on this, the biologist is able to estimate that, rounding to the nearest deer, only deer are being killed by the disease each month.

A biologist noticed that a small forest has a population of deer that naturally grows according to the logistic model y' = 0.0005y(300 – y) where y is the number of deer at time t measured in months. The carrying capacity of this forest is deer. In January 2021, a disease began killing the deer at a rate of 10 deer per month. If there were 110 deer in the pond when the biologist first noticed the disease (at time t = 0)), then the number of deer w and reach in increase the long run. decrease After many months, the biologist finds that the disease is not affecting the deer as much and fewer deer are dying from it each month. The deer population has rebounded and is now at a stable size of 270. Based on this, the biologist is able to estimate that, rounding to the nearest deer, only deer are being killed by the disease each month.

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

A biologist noticed that a small forest has a population of deer that naturally
grows according to the logistic model y' = 0.0005y(300 – y) where y is the
number of deer at time t measured in months. The carrying capacity of this
forest is
deer.
In January 2021, a disease began killing the deer at a rate of 10 deer per month.
If there were 110 deer in the pond when the biologist first noticed the disease (at
time t =
0)), then the number of deer w
and reach
in
increase
the long run.
decrease
After many months, the biologist finds that the disease is not affecting the deer
as much and fewer deer are dying from it each month. The deer population has
rebounded and is now at a stable size of 270. Based on this, the biologist is able
to estimate that, rounding to the nearest deer, only
deer are being killed
by the disease each month.

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