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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!

Guest Mar 6, 2019

#1**+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

CPhill Mar 6, 2019