Mathematical Models and Numerical Methods: Population Models

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July 16th 2007, 04:11 PM
googoogaga

Mathematical Models and Numerical Methods: Population Models

These homework problems that I need help on are due in two days (Wednesday Morning, eastern standard time, so it's not really urgent), I would put on the urgent link but two days is not that urgent, I think. In the meantime I will attempt to work at them and compare my work with yours once you help me). Anyways here they are:

1) Solve the initial value problem: dx/dt = 1- x^(2), x(0)= 3

2) The world population in 1990 was 5,274.320M and in 2000 was 6,073.265M. Predict the world population in 2007 and 2050 by using the Unbounded Population Model. Is your answer greater, lesser, or equal to
the current world population posted on
U.S. and World Population Clocks - POPClocks (Solve w/o Maple)

3) the world population in 1980 was 4,447.068M, in 1990 was 5,274.320M
and in 2000 was 6,073.265M. Predict the world population in 2007 and
2050 by using the Bounded Population Model. Also, what is the limiting
population (carrying capacity) of the world? (Solve w/o Maple).
July 16th 2007, 07:48 PM
CaptainBlack

Quote:

Originally Posted by googoogaga

These homework problems that I need help on are due in two days (Wednesday Morning, eastern standard time, so it's not really urgent), I would put on the urgent link but two days is not that urgent, I think. In the meantime I will attempt to work at them and compare my work with yours once you help me). Anyways here they are:

1) Solve the initial value problem: dx/dt = 1- x^(2), x(0)= 3

This is of variables seperable type, so we can write:

$ \int \frac{1}{1-x^2}~dx=\int ~dt $

Quote:

2) The world population in 1990 was 5,274.320M and in 2000 was 6,073.265M. Predict the world population in 2007 and 2050 by using the Unbounded Population Model. Is your answer greater, lesser, or equal to
the current world population posted on
U.S. and World Population Clocks - POPClocks (Solve w/o Maple)

Now I would guess by the "Unbounded Population Model" you mean the
exponetial grown model:

$ \frac{dP}{dt}=rP $

but you should confirm that this is what is meant.

Quote:

3) the world population in 1980 was 4,447.068M, in 1990 was 5,274.320M
and in 2000 was 6,073.265M. Predict the world population in 2007 and
2050 by using the Bounded Population Model. Also, what is the limiting
population (carrying capacity) of the world? (Solve w/o Maple).

Sounds as though this is the logistic growth model:

$ \frac{dP}{dt}=rP\left( 1-\frac{P}{K}\right) $

where $K$ is the carrying capacity.

RonL
July 17th 2007, 05:11 AM
googoogaga

Reply for Captain Black: Unbounded Population Growth Model and Logistic Growth Model

Those two equations you gave me for the two last problem are indeed correct based on the class notes I've taken. Right on!:D