Malthus' Principle of Population Growth: Solving a Differential Equation

In summary, Malthus' principle of population growth can be represented by the differential equation y'=ky, where y(t) is the population t years after the initial measurement and k is the growth constant. The solution to this equation is y(t)=Ae^{kt}, where A is the initial amount. To determine the annual percent increase in the population, use the value of k in the equation and calculate the percentage change from the initial amount. This demonstrates that while the amount of increase may vary, the percentage of increase remains constant.
  • #1
notme
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Malthus' principle of population growth can be written as the differential equation

y'=ky

where y(t) is the population t years after the initial measurement and k is the growth constant. The solution to this differential equation is given by

y(t)=Ae^{kt}

where A is the initial amount. If k = 0.03, determine the annual percent increase in y.

The % of increse changes every year... I don't know what to do.
 
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  • #2
If the population is A this year, according to your equation, it should be Aek next year. How great an increase is that? What percentage of the original population is that increase? The whole point of this problem is that while the amount of increase changes every year, the percentage of increase does NOT!
 

Related to Malthus' Principle of Population Growth: Solving a Differential Equation

What is Malthus' Principle of Population Growth?

Malthus' Principle of Population Growth is a theory proposed by Thomas Malthus in the late 18th century. It states that the human population grows at a geometric rate, while the production of food and resources grows at an arithmetic rate. This leads to a population that exceeds the available resources, resulting in famine, disease, and other natural checks on population growth.

What is the differential equation used to represent Malthus' Principle of Population Growth?

The differential equation used to represent Malthus' Principle of Population Growth is dN/dt = rN, where N represents the population size, t represents time, and r is the rate of population growth. This equation assumes that the rate of population growth is directly proportional to the current population size.

How does Malthus' Principle of Population Growth apply to real-world populations?

Malthus' Principle of Population Growth has been used to explain the dynamics of real-world populations, particularly in areas where resources are limited. It has been applied to human populations, as well as populations of other species, to understand how population growth is affected by factors such as food availability, disease, and environmental conditions.

What criticisms have been raised against Malthus' Principle of Population Growth?

One of the main criticisms against Malthus' Principle of Population Growth is that it does not take into account technological advancements and improvements in agricultural practices, which have allowed for an increase in food production and have helped to support a larger population. Additionally, some critics argue that Malthus' theory is too simplistic and does not consider other factors that influence population growth, such as social and economic factors.

How has Malthus' Principle of Population Growth influenced modern population studies?

Malthus' Principle of Population Growth has played a significant role in shaping modern population studies and theories. It has been used as a basis for understanding population dynamics, and has influenced the development of other theories, such as the demographic transition theory. While Malthus' theory has been challenged and modified over time, it remains an important concept in the study of population growth and sustainability.

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