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Name ___________________
ChE 2120 Final Exam
December 8, 2004
•
In all problems, you should use numerical methods you learned in class to solve
the problems, and must show all your work.
•
You do not need to wait for methods to converge, but instead may perform three
iterations only.
•
There are five problems, and each problem is worth 20 pts.
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The logistic model is used to simulate population as in
p
p
p
k
dt
dp
gm
)
/
1
(
max
−
=
where
p
= population,
k
gm
= the maximum growth rate under unlimited conditions,
and
p
max
= the carrying capacity.
Simulate the world’s population from 1960 to
2000.
Employ the following initial conditions and parameter values for your
simulation:
p
0
(in 1960) = 3,040 million people,
k
gm
= 0.026/yr, and
p
max
= 12,000
million people.
Have the function generate output corresponding to the dates for
the following measured population data.
Use the results to compute the sum of
the squares of the residuals between the data and the simulation output.
t
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 Summer '07
 Gallivan

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