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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.
Stacey Warren - Expert brainly.com
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No idea how to set this out.
The numbers are relatively easy to figure out. But how to set up the transition matrix ...
I wonder if you've seen this video yet: www.youtube.com/watch?v=VeTjArt51Q4
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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.
If I got the matrix right I understand what to do next
T^10 x initial state matrix.
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.
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.
What do you think about setting out the worded problem and solving by cancelling out? Could that work?
And then typing in the simplified data into the matrix.
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.
No problem mate. Thanks anyway.
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
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.