Information Technology Reference
In-Depth Information
(k) Show that the requirement
@F
@˛
@F
@
D
D
0
leads to the linear equations
10˛
C
9
X
nD0
!
D
9
X
d
n
c
n
nD0
(5.166)
9
X
!
˛
C
9
X
nD0
!
D
9
X
d
n
d
n
c
n
d
n
:
nD0
nD0
(l) Solve the linear system (
5.166
) with respect to ˛ and .Verifythat
˛
0:0368
and
0:0040:
(5.167)
(m) Use the fact that
D
˛=ˇ to show that
ˇ
9:2 :
(5.168)
(n) Show that the solution of the logistic model with an initial data y
0
D
6:08,
which corresponds to the population on the Earth in the year 2000, is given by
55:94
6:08
C
3:12 e
0:0368 t
y.t/
D
:
(5.169)
(o) Plot y.t/ given by (
5.169
)andp.t/ given by (
5.101
).