Answer Question 2 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.

Name: Answer Question 2 pls 1. The population model given in class fails to
Uploaded: 2024-03-20T07:06:41.000Z
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Description: Answer Question 2 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 poplationchan

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The rate at which the population changes is a net rate.
The net rate is the…

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