A television campaign is conducted during the football season to promote a well-known brand
x
shaving cream. For each of several weeks, a survey is made, and it is found that each week,
90%
of those using brand
x
continue to use it and
10%
switch to another brand. It is also found that of those not using brand
x,10%
switch to brand
x
while the other
90%
continue using another brand. (A) Draw a transition diagram. (B) Write the transition matrix. (C) If
20%
of the people are using brand
x
at the start of the advertising campaign, what percentage will be using it 1 week later? 2 weeks later? (Type integers or decimals. Do not include the
%
symbol in your answer.) (B) Write the transition matrix, P. Let
A
be the state in which people use brand
x
. (Type an integer or a decimal for each matrix element.) (C) The percentage of people using brand
x1
week after the start of the advertising campaign is %. (Type an integer or a decimal.)