Answer Quetion 5 pls 1. The population model given in class fails to take death into consideration; the growth rate equals the birth rate.In another model of a changing population of a community it is assumed that the rate at which the poplationchanges is a net rate-that is, the difference between the rate of births and the rate of deaths in the community.Determine a model for the population P(t) if both the birth rate and the death rate are proportional to thepopulation present at time t.2. Using the concept of net rate above, determine a model for a population P(t) if the birth rate is proportional tothe population present at time t but the death rate is proportional to the square of the population present at timet.3. At a time denoted as t = 0 a technological innovation is introduced into a community that has a fixed populationof n people. Determine a differential equation for the number of people x(t) who have adopted the innovation attime t if it is assumed that the rate at which the innovations spread through the community is jointly proportionalto the number of people who have adopted it and the number of people who have not adopted it.dP= (k cos t) P, where k is a positive constant, is a model of human population P(t)4. The differential equationof a certain community. Discuss an interpretation for the solution of this equation. In other words, what kind ofpopulation do you think the differential equation describes?dt5. For high-speed motion through the air-such as a skydiver falling before the parachute is opened-air resistanceis closer to a power of the instantaneous velocity v(t). Determine a differential equation for the volocity v(t) ofa falling body of mass m if air resistance is proportional to the square of the instantaneous velocity.

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Description: Answer Quetion 5 pls 1. The population model given in class fails to take death into consideration; the growth rate equals the birth rate.In another model of a changing population of a community it is assumed that the rate at which the poplationchang

We have to Determine a differential equation for the velocity v(t) Of a falling body of mass m if…

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5. For high-speed motion through the air-such as a skydiver falling before the parachute is opened-air resistance is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the volocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity.

5. For high-speed motion through the air-such as a skydiver falling before the parachute is opened-air resistance is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the volocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity.

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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Answer Quetion 5 pls

1. The population model given in class fails to take death into consideration; the growth rate equals the birth rate.
In another model of a changing population of a community it is assumed that the rate at which the poplation
changes is a net rate-that is, the difference between the rate of births and the rate of deaths in the community.
Determine a model for the population P(t) if both the birth rate and the death rate are proportional to the
population present at time t.
2. Using the concept of net rate above, determine a model for a population P(t) if the birth rate is proportional to
the population present at time t but the death rate is proportional to the square of the population present at time
t.
3. At a time denoted as t = 0 a technological innovation is introduced into a community that has a fixed population
of n people. Determine a differential equation for the number of people x(t) who have adopted the innovation at
time t if it is assumed that the rate at which the innovations spread through the community is jointly proportional
to the number of people who have adopted it and the number of people who have not adopted it.
dP
= (k cos t) P, where k is a positive constant, is a model of human population P(t)
4. The differential equation
of a certain community. Discuss an interpretation for the solution of this equation. In other words, what kind of
population do you think the differential equation describes?
dt
5. For high-speed motion through the air-such as a skydiver falling before the parachute is opened-air resistance
is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the volocity v(t) of
a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity.

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