A population P(t) of field mice, where P is the number of mice and t is measuredin months from some starting point, grows at the rate of 50% per month. However, owls in theneighbourhood eat them at the rate of 600/month. A model for the mice population is given by thedifferential equationdP= 0.5P – 600dtIf the field can only sustain a capacity population of k = 10000 field mice, can you state a bettermodel for the mice population in which populations do not grow to infinity?

Name: A population P(t) of field mice, where P is the number of mice and t
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Description: A population P(t) of field mice, where P is the number of mice and t is measuredin months from some starting point, grows at the rate of 50% per month. However, owls in theneighbourhood eat them at the rate of 600/month. A model for the mice populat

Answered: A population P(t) of field mice, where…

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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A population P(t) of field mice, where P is the number of mice and t is measured
in months from some starting point, grows at the rate of 50% per month. However, owls in the
neighbourhood eat them at the rate of 600/month. A model for the mice population is given by the
differential equation
dP
= 0.5P – 600
dt
If the field can only sustain a capacity population of k = 10000 field mice, can you state a better
model for the mice population in which populations do not grow to infinity?

Expert Solution

Step 1

Given that a population $P (t)$ of field mice, where $P$ is the number of mice and $t$ is the measured in months from starting point at the rate of 50% per month. So, the growth rate is

$r = 0.5$

Owls in the neighborhood eat them at the rate of 600 per month which is constant.

The field can only sustain a capacity population of $κ = 10, 000$ . therefore, maximum carrying capacity is $κ = 10, 000$ .

Since, there is a maximum carrying capacity, it restricts the growth due to lack of available resources or other reason. In that case, population do not grow to infinity.

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