LAB #5
Population Models
Goal
: Compare various population models for the population of New York over the last
200 years.
Required tools
:
Matlab
routines
plot
,
norm
,
fplot
; separable differential equations.
Discussion
This lab compares three models of population growth:
(
*
)
dP
dt
=
r
(Linear Growth)
(
**
)
dP
dt
=
rP
(Exponential Growth)
(
***
)
dP
dt
=
rP
1

P
K
(Logistic Growth)
P
(
t
) is the population at time
t
(
r
and
K
are positive constants).
The following table lists the population of New York State in 10 year intervals from
the year 1790 to 1990:
Population of New York (in thousands)
Year
1790
1800
1810
1820
1830
1840
1850
1860
1870
1880
Pop.
379
423
472
523
610
738
995
1231
1457
1783
Year
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
Pop.
2239
2805
3366
3852
4250
4317
4691
5149
5689
5737
6016
Assignment
(1)
Use
Matlab
to plot the population given in the table as a function of
T
where
T
is measured in decades. Thus
T
= 0 corresponds to the year 1790 and
T
= 20
corresponds to 1990.
1
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(i) Data in
Matlab
is stored in matrices (in fact
Matlab
is short for “
Mat
rix
Lab
oratory”). Enter the time matrix
T
and the actual population matrix
A
into
Matlab
as follows:
>>
T
= [
0
,
1
,
2
,
· · ·
,
20
];
>>
A
= [
379
,
423
,
472
,
· · ·
,
6016
];
(The semicolons “;” prevent
Matlab
from displaying the entries on the
screen.) A quick way to produce the matrix
T
is
>> T
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 Spring '08
 CHO
 matlab, Equations, ZOOM, Caroline Botelho, WGBHTV

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