/sci/ - Science & Math » Thread #13295523

27KiB, 530x530, USA-carrying-capacity.png

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You Should Be Able To Solve This

OP Sat 19 Jun 03:17:30 2021 No.13295523 View Reply Original Report

Quoted By: >>13296143 >>13297984 >>13298067

Solve for USA Carrying Capacity (the maximum sustainable population, "K") using the logistic model provided at:
https://sites.math.northwestern.edu/~mlerma/courses/math214-2-03f/notes/c2-logist.pdf
...and the Census data from:
https://www.census.gov/programs-surveys/decennial-census/decade.html

Anonymous

Anonymous Sat 19 Jun 2021 04:30:40 No.13295697 Report

Quoted By: >>13295723 >>13295739 >>13296136 >>13298067

The carrying capacity changes as technology changes, moron. K is not constant.

Anonymous

Anonymous Sat 19 Jun 2021 04:44:00 No.13295723 Report

Quoted By: >>13295739

>>13295697
The carrying capacity is part of the model, moron. K is an estimate.

Anonymous

Anonymous Sat 19 Jun 2021 04:52:25 No.13295739 Report

Quoted By: >>13295750

>>13295697
>723?
>>>13295697
>>13295723
morons kys

Anonymous

Anonymous Sat 19 Jun 2021 05:00:59 No.13295750 Report

Quoted By:

>>13295739
>morons kys
no U

Anonymous

Anonymous Sat 19 Jun 2021 07:43:28 No.13296106 Report

Quoted By: >>13296136

Wait can you use this predict future????

Anonymous

Anonymous Sat 19 Jun 2021 07:56:20 No.13296136 Report

Quoted By:

>>13296106
Yes, but this simple model cannot anticipate significant technology changes,
as mentioned by this moron:
>>13295697

Anonymous

Anonymous Sat 19 Jun 2021 07:59:28 No.13296143 Report

Quoted By: >>13296145

>>13295523
Fuck off, we're full.

Anonymous

Anonymous Sat 19 Jun 2021 08:00:04 No.13296145 Report

Quoted By:

>>13296143
>we're full of shit
FTFY

OP Sat 19 Jun 2021 20:01:01 No.13297984 Report

Quoted By: >>13298035

>>13295523
Let t=40 and $P_40=331.45$
and $\displaystyle A= \frac{K-226.54}{226.54}$
then $\displaystyle 331.45= \frac{K}{1+(K-226.54)e^{-40k}/226.54}$
and solve for $\displaystyle e^{-40k}= \frac{226.54(K-331.45)}{331.45(K-226.54)}$
Let t=20 and $P_20=281.42$
and $\displaystyle A= \frac{K-226.54}{226.54}$
then $\displaystyle 281.42= \frac{K}{1+(K-226.54)e^{-20k}/226.54}$
and solve for $\displaystyle e^{-20k}= \frac{226.54(K-281.42)}{281.42(K-226.54)}$
Notice $e^{-40k}=(e^{-20k})^2$
so $\displaystyle \frac{226.54(K-331.45)}{331.45(K-226.54)}= \left [ \frac {226.54(K-281.42)}{281.42(K-226.54)} \right ]^2$

OP Sat 19 Jun 2021 20:05:18 No.13298006 Report

Quoted By: >>13298116

Let t=40 and $P_{40}=331.45$
and $\displaystyle A= \frac{K-226.54}{226.54}$
then $\displaystyle 331.45= \frac{K}{1+(K-226.54)e^{-40k}/226.54}$

and solve for $\displaystyle e^{-40k}= \frac{226.54(K-331.45)}{331.45(K-226.54)}$
Let t=20 and $P_{20}=281.42$
then $\displaystyle 281.42= \frac{K}{1+(K-226.54)e^{-20k}/226.54}$

and solve for $\displaystyle e^{-20k}= \frac{226.54(K-281.42)}{281.42(K-226.54)}$
Notice $e^{-40k}=(e^{-20k})^2$
so $\displaystyle \frac{226.54(K-331.45)}{331.45(K-226.54)}= \left [ \frac {226.54(K-281.42)}{281.42(K-226.54)} \right ]^2$

Anonymous

Anonymous Sat 19 Jun 2021 20:10:21 No.13298035 Report

Quoted By: >>13298116

>>13297984
So what you are saying is...

Anonymous

Anonymous Sat 19 Jun 2021 20:17:55 No.13298067 Report

Quoted By:

>>13295523
>>13295697
Technological related increases to carrying capacity have largely leveled off since the 90s. These days changes are more a result of changes in availability of natural resources such as water and minerals.

This will become painfully obvious if California's drought continues for much longer.

Anonymous

Anonymous Sat 19 Jun 2021 20:22:12 No.13298085 Report

Quoted By:

I alway wondered how tf does the Arithmetic and geometry sequence in my Calculus usage irl until I read this post

OP Sat 19 Jun 2021 20:28:50 No.13298116 Report

Quoted By:

>>13298035
I re-formatted 13297984 to be a bit more legible as
>>13298006
showing the steps to get a more-tractable algebraic equation from the two logistic equations.

Anonymous

Anonymous Sat 19 Jun 2021 20:34:56 No.13298138 Report

Quoted By: >>13298161

>muh doomday scenario
>muh fake equations pulled out of thin air with no justification
>woe is me, the world is coming to an end and i have to save it
conscienceless attention hungry loser with delusions of grandeur trying to pull a fast one
https://en.wikipedia.org/wiki/Messiah_complex

Anonymous

View Same Google iqdb SauceNAO back-to-reddit.png, 46KiB, 250x175

Anonymous Sat 19 Jun 2021 20:42:32 No.13298161 Report

Quoted By:

>>13298138
>paranoid schizophrenic with no knowledge nor interest in /sci/ence
GTFO

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