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mathsashelp
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A very small country town has a population that can be grouped according to three categories: adults teenagers and children.
Each year statistics show that:
Children are born at the rate of 4% of the adult population 12% of children become teenagers 15% of teenagers become adults 0.5% of children die 3% of teenagers die 8% of adults die
Presuming that the town started with 350 children, 640 teenagers and 2100 adults, find how many there will be of each category after 10 years.
I'm having trouble finding the transition matrix.
So far I've got.
c t a d
c [0.875 0 0.04 0]
t [ 0.12 0.082 0 0]
a [ 0 0.15 0,88 0]
d [ 0.005 0.03 0.08 0]
The textbook somehow gets 0.04 in the 4th row of the 3rd column instead of 0.08 and has a 1 in the 4th row of the 4th column instead of 0.
Not sure how or why.
If I could get the Transition matrix correct I understand that it would simply be
T^10 x initial state but I'm just having trouble setting it out.
Thanks
Each year statistics show that:
Children are born at the rate of 4% of the adult population 12% of children become teenagers 15% of teenagers become adults 0.5% of children die 3% of teenagers die 8% of adults die
Presuming that the town started with 350 children, 640 teenagers and 2100 adults, find how many there will be of each category after 10 years.
I'm having trouble finding the transition matrix.
So far I've got.
c t a d
c [0.875 0 0.04 0]
t [ 0.12 0.082 0 0]
a [ 0 0.15 0,88 0]
d [ 0.005 0.03 0.08 0]
The textbook somehow gets 0.04 in the 4th row of the 3rd column instead of 0.08 and has a 1 in the 4th row of the 4th column instead of 0.
Not sure how or why.
If I could get the Transition matrix correct I understand that it would simply be
T^10 x initial state but I'm just having trouble setting it out.
Thanks
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