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FYI: The problem is supposed to say "The bluegill population in a pond can be modeled by the function given.

Just help me find the answer to each question, and show me how I would find each answer. Thanks!

 Mar 6, 2019
 #1
avatar+98060 
+2

I know a few

 

1.  y intercept....let t = 0    and we have that

 

y =   1000 / [ 1 + 9e^(-.4(0)) ]    =  1000/ [ 1 + 9(1) ]  =  1000/ 10   = 100

 

 

2.     asymptotes

 

No  vertical asymptotes since  the exponential in the denominator is never  negative....so....the denominator is never = 0

 

Horizontal asymptote........as t gets larger and larger, the exponential at the bottom approaches 0

So.....the horizontal asymptote is

y =  1000 /  [ 1 + 0 ]   =  1000

 

 

3. Don't know this one

 

4. After 15 years...there will be   1000 / [ 1 + 9e^(-.4 * 15) ]  ≈  978  bluegills

 

 

cool  cool  cool 

 Mar 6, 2019
 #3
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+1

CPhill, how did you calculate that 100/1+9e^(-0.4(15)) is approx equal to 978?

Guest Mar 7, 2019
 #4
avatar+99230 
+2

CPhill, how did you calculate that 100/1+9e^(-0.4(15)) is approx equal to 978?

 

CPhill did not say   100/    he said   1000/

 

 

1000/(1+9*e^(-0.4*15)) = 978.1780512369621114

Melody  Mar 7, 2019
 #2
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If I'm not mistaken, the point of maximum growth should be the point at which the bluegill population stops growing(presumably), so I guess the best bet would be either to skip that problem, or graph it out somehow and then approximate it :P 

 Mar 6, 2019

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