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Sketch solution curve of differential equation

Initially N=100, the rate increase of N is 8 per year. In one theory being tested, the number N of nesting pairs after t years is assumed to satisfy d.e: dN/dT = 1/5000(N)(500-N)
When N=300 dN/dT = 12
When N=450 dN/dT = 4.5

Using this data sketch the solution curve of the differential eq. for which N=100 when t=0



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Original post by TSRforum
Initially N=100, the rate increase of N is 8 per year. In one theory being tested, the number N of nesting pairs after t years is assumed to satisfy d.e: dN/dT = 1/5000(N)(500-N)
When N=300 dN/dT = 12
When N=450 dN/dT = 4.5

Edit: Describe what happens as N approaches 500 and interpret your answer.

Using this data sketch the solution curve of the differential eq. for which N=100 when t=0



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Original post by TSRforum


What happens when N=500? Does the derivative become a certain value? What can you interpret about that value?
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Original post by Zacken
What happens when N=500? Does the derivative become a certain value? What can you interpret about that value?


It becomes 0 but what can I interpret from that?


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Original post by TSRforum
It becomes 0 but what can I interpret from that?


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What do you call points whose derivative is 0?
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Original post by Zacken
What do you call points whose derivative is 0?


Can't remember... Symmetrical? 😣


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Original post by TSRforum
Can't remember... Symmetrical? 😣


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Stationary points.
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Original post by Zacken
Stationary points.


So N reached MAX point as it gets bigger?


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Original post by TSRforum
So N reached MAX point as it gets bigger?


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Yep. Also, the 'y'-axis intercept is going to be 100.
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So something like this...http://imgur.com/a/H6Rcq?



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