dehelloo
  • dehelloo
Need help with Transition Matrices - Test soon 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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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dehelloo
  • dehelloo
No idea how to set this out.
Hero
  • Hero
The numbers are relatively easy to figure out. But how to set up the transition matrix ...
Hero
  • Hero
I wonder if you've seen this video yet: www.youtube.com/watch?v=VeTjArt51Q4

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dehelloo
  • dehelloo
I was thinking 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] mate what do you think about this? I just logically filled out the rest. however the 4 column with all 0's im a bit unsure about. And yes ahaha I listened to that Australian dude last night. It's just this situation is a little more complex. Thanks though.
dehelloo
  • dehelloo
If I got the matrix right I understand what to do next T^10 x initial state matrix.
Hero
  • Hero
I agree. It appears to be more Complex than what the video explains. I can't promise that what you've done is correct or not though.
dehelloo
  • dehelloo
It's just setting out the matrix is a bit dodgy. I cant get it right. The text book 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.
dehelloo
  • dehelloo
What do you think about setting out the worded problem and solving by cancelling out? Could that work?
dehelloo
  • dehelloo
And then typing in the simplified data into the matrix.
Hero
  • Hero
TBH it's really late for me. This question is more complete than what I assumed initially. Furthermore, I don't have the proper tools to engage as much as I want to. Don't worry. There's Someone around Who can help. You might want to try asking your question on Quora.
Hero
  • Hero
Complex *
dehelloo
  • dehelloo
No problem mate. Thanks anyway.
Rhystic
  • Rhystic
I came up with something similar but a bit different: c | t | a | d c [ .875 | 0 | .04 | 0 _ t [.12 | .82| 0 | 0 _ a [0 |.15 | .92| 0 _ d [.005 | .03 | .08 | 0 Basically from yours for row t I have .82 instead of .082 (I think maybe you just typod) ; For row a column a I have .92 instead of .88 because even though 4 percent of adults are childs being born, adults cannot backtrack into children. so you only subtract adults to death which is .08 . Give me a sec to type the proof
Rhystic
  • Rhystic
Yeah I believe thats right, because vertically all the populations sum up to 1.0 except for adults which has a small surplus do to children being born. horizontally you get .915 ; .94 ; 1.07 ; .115 which makes sense because the entire population does not stay as children, and youll have a larger amount of adult population than the inital adult population because the amount of teenagers turning into adults vs adults dieing is higher.

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