SOLUTION: Can someone please assist in explaining this problem. I still do not understand what I am doing or why I am doing it. The population P of a fish farm in t years is modeled by

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Can someone please assist in explaining this problem. I still do not understand what I am doing or why I am doing it. The population P of a fish farm in t years is modeled by      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1129785: Can someone please assist in explaining this problem. I still do not understand what I am doing or why I am doing it.

The population P of a fish farm in t years is modeled by the equation
P(t) = 1600/ 1 + 9e−0.9t.
To the nearest whole number, what will the fish population be after 2 years?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P%28t%29+=+1600+%2F+%28+1+%2B+%289e+%29%5E%28-.9t%29%29+ ( If this is correct )
+P%282%29+=+1600+%2F+%28+1+%2B+%289e+%29%5E%28-.9%2A2%29%29+
+P%282%29+=+1600+%2F+%28+1+%2B+%289e%29%5E%28-1.8%29+%29+
* now I have to use calculator *
+P%282%29+=+1600+%2F+%28+1+%2B+.0031668+%29+
+P%282%29+=+1594.95+
1,595 after 2 yrs ( if I got the equation right )

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


In fact the other tutor does NOT have the equation right. It is a standard logistic equation:

P%28t%29+=+1600%2F%281%2B9e%5E%28-0.9t%29%29

In a logistic equation, it is easy to calculate the beginning value (t=0) and the limiting value (t "very large"):

t=0: 1600%2F%281%2B9e%5E0%29+=+1600%2F%281%2B9%29+=+1600%2F10+=+160

t=1000:

For intermediate values, with the exponential base e and a decimal exponent, you need to use a calculator.

P%282%29+=+1600%2F%281%2B9e%5E%28-0.9%282%29%29%29 = 643 to the nearest whole number.