Exponential and Logarithmic Applications

[AnimeFan]

A certain lake is stocked with fish. The population is growing according to the logistic curve: P = 10,000/1+9e^-0.2t where t is measured in months since the lake was initially stocked.

What is the long term behavior of this function? (Is there a maximum possible population?) Use Algebra, a graph, or a table to justify your answer.

 

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[Steven G]

What happens to P as t goes to infinity?

 

[BigBeachBanana]

What happens to P as t goes to infinity?

The instruction states: "Use Algebra, a graph, or a table to justify your answer". I believe that using limit falls under calculus.

The OP is missing parenthesis, I assume P should be:
[math]P = \frac{10,000}{1+9e^{-0.2t}}[/math]

 

[Steven G]

The instruction states: "Use Algebra, a graph, or a table to justify your answer". I believe that using limit falls under calculus.

The OP is missing parenthesis, I assume P should be:
[math]P = \frac{10,000}{1+9e^{-0.2t}}[/math]

I don't think that you need the formal definition of a limit or any experience using limits to figure out what the function P is approaching as t gets larger and larger.
To use Algebra or a table would require you to input large values of t into the function. To use a graph, you'd need to know how to decide what P is approaching as t gets large.