Information Technology Reference
In-Depth Information
Tabl e 5. 3
The calculated
values of b
n
using (
5.80
)
based on the numbers of the
world's population from 1950
to 1955
100
p.n
C
1/
p.n/
Year
np /
n
D
p.n/
1950
0
2.555
1.49
1951
1
2.593
1.62
1952
2
2.635
1.71
1953
3
2.680
1.79
1954
4
2.728
1.91
1955
5
2.780
Based on the results in Table
5.3
, we want to compute a constant approximation
to b. We use the arithmetic average, see (
5.1
)-(
5.5
), and define
4
X
1
5
1
5
.1:49
C
1:62
C
1:71
C
1:79
C
1:91/
D
1:704:
b
D
b
n
D
nD0
Since
D
100
p.n
C
1/
p.n/
p.n/
b
n
D
100 ˛
n
;
(5.81)
we define
1
100
b
D
0:01704:
˛
D
(5.82)
Recall that the solution of (
5.76
)isgivenby
p.t/
D
p
0
e
˛t
;
so we have
p.t/
D
2:555 e
0:01704 t
:
(5.83)
Since the year 2000 corresponds to t
D
50,wehave
p.50/
D
2:555 e
0:0170450
5:990:
(5.84)
This should be compared with the actual population in the year of 2000, which is
6.080 billion. So the relative error is
6:080
5:990
6:080
100%
D
1:48%:
(5.85)
Based on the population of 1950-1955, we computed the number of people living
on the Earth in the year 2000 with an error of about 1:5%. That is quite remarkable!
