Problems 61-70 refer to the following transition matrix P and its powers A B C P = A B C .6 .3 .1 .2 .5 .3 .1 .2 .7 A B C P 2 = A B C .43 .35 .22 .25 .37 .38 .17 .27 .56 A B C P 3 = A B C .35 .348 .302 .262 .336 .402 .212 .298 .49 Using a graphing calculator to compute powers of P , find the smallest positive integer n such that the corresponding entries in P n and P n + 1 are equal when rounded to three decimal places.
Problems 61-70 refer to the following transition matrix P and its powers A B C P = A B C .6 .3 .1 .2 .5 .3 .1 .2 .7 A B C P 2 = A B C .43 .35 .22 .25 .37 .38 .17 .27 .56 A B C P 3 = A B C .35 .348 .302 .262 .336 .402 .212 .298 .49 Using a graphing calculator to compute powers of P , find the smallest positive integer n such that the corresponding entries in P n and P n + 1 are equal when rounded to three decimal places.
Solution Summary: The author explains how to approximate the smallest positive integer n such that the entries of
Problems 61-70 refer to the following transition matrix
P
and its powers
A
B
C
P
=
A
B
C
.6
.3
.1
.2
.5
.3
.1
.2
.7
A
B
C
P
2
=
A
B
C
.43
.35
.22
.25
.37
.38
.17
.27
.56
A
B
C
P
3
=
A
B
C
.35
.348
.302
.262
.336
.402
.212
.298
.49
Using a graphing calculator to compute powers of
P
, find the smallest positive integer
n
such that the corresponding entries in
P
n
and
P
n
+
1
are equal when rounded to three decimal places.
A tank contains 60 kg of salt and 2000 L of water. Pure water enters a tank at the rate 8 L/min. The
solution is mixed and drains from the tank at the rate 11 L/min.
Let y be the number of kg of salt in the tank after t minutes.
The differential equation for this situation would be:
dy
dt
y(0) =
Simplify the below expression.
3 - (-7)
Solve the initial value problem:
y= 0.05y + 5
y(0) = 100
y(t) =
Chapter 9 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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