SOLUTION: Can someone help? The population P of a fish farm in t years is modeled by the equation P(t) = 1500/ 1 + 9e^(−0.8t). To the nearest tenth, how many years will it take for

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Question 1139494: Can someone help?
The population P of a fish farm in t years is modeled by the equation
P(t) = 1500/ 1 + 9e^(−0.8t).
To the nearest tenth, how many years will it take for the population to reach 900?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The population P of a fish farm in t years is modeled by the equation

P%28t%29+=+1500%2F+%281+%2B+9e%5E%28-0.8t%29%29+

To the nearest tenth, how many years will it take for the population to reach 900?

=> given P%28t%29+=900

900+=+1500%2F+%281+%2B+9e%5E%28-0.8t%29%29+
1+%2B+9e%5E%28-0.8t%29+=+1500%2F900+
9e%5E%28-0.8t%29+=+5%2F3-1+
9e%5E%28-0.8t%29+=+2%2F3
e%5E%28-0.8t%29+=+%282%2F3%29%2F9
+e%5E%28-0.8t%29+=+2%2F27...take natural log
ln%28e%5E%28-0.8t%29+%29=+ln%282%2F27%29
%28-0.8t%29+ln%28e+%29=+ln%282%29-ln%283%5E3%29
-0.8t+%2A1=+ln%282%29-3ln%283%29
-0.8t+=-2.6
t=-2.6%2F%28-0.8%29
t≈3.3 years will it take for the population to reach 900