SOLUTION: Would someone help? The population P of a fish farm in t years is modeled by the equation P(t) = 1500/ 1 + 8e^(−0.9t) What is the carrying capacity for the fish population?

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Question 1139495: Would someone help?
The population P of a fish farm in t years is modeled by the equation
P(t) = 1500/ 1 + 8e^(−0.9t)
What is the carrying capacity for the fish population?
Answer by greenestamps(13196) About Me  (Show Source):
You can put this solution on YOUR website!


Use parentheses where required! The equation is not P(t) = 1500/ 1 + 8e^(−0.9t) --> P%28t%29+=+1500%2F1%2B8e%5E%28-0.9t%29

The equation is P(t) = 1500/ (1 + 8e^(−0.9t)) --> P%28t%29+=+1500%2F%281%2B8e%5E%28-0.9t%29%29

The carrying capacity is the value of the logistic function for large values of t.

For large values of t, the exponential e%5E%28-0.9t%29 approaches 0; the value of the function then is

1500%2F%281%2B0%29+=+1500%2F1+=+1500