SOLUTION: Could someone please explain and demonstrate the method that should be used to solve the equation. Thanks. The population P of a fish farm in t years is modeled by the equation

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Could someone please explain and demonstrate the method that should be used to solve the equation. Thanks. The population P of a fish farm in t years is modeled by the equation       Log On


   

Question 1129925: Could someone please explain and demonstrate the method that should be used to solve the equation. Thanks.
The population P of a fish farm in t years is modeled by the equation
P(t) = 1700/ 1 + (9^ e−0.7t)
To the nearest tenth, how long 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!

P%28t%29+=+1700%2F+%281+%2B+%289%5E+%28e-7t%29%29%29

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


900=+1700%2F+%281+%2B+%289%5E+%28e-0.7t%29%29%29

900%281+%2B+9%5E+%28e-0.7t%29%29=+1700+

1+%2B+9%5E+%28e-0.7t%29=+1700%2F900+

9%5E+%28e-0.7t%29=+17%2F9-1+

9%5E+%28e-0.7t%29=+17%2F9-9%2F9+

%283%5E2%29%5E+%28e-0.7t%29=+8%2F9+

3%5E+%282%28e-0.7t%29%29=+8%2F9+.....take log of both sides

log%283%5E%282%28e-0.7t%29%29%29=+log%288%2F9%29+

%282%28e-0.7t%29%29log%283%29=+log%282%5E3%29-log%283%5E2%29+

%282%28e-0.7t%29%29log%283%29=+3log%282%29-2log%283%29+

e-0.7t=+%283log%282%29%29%2F%282log%283%29%29-2log%283%29%2F2log%283%29+

e-0.7t=+%283log%282%29%29%2F%282log%283%29%29-1+

2.71828+-+0.7t=+0.9463946303571-1+

2.71828+-+0.7t=-0.0536053696428+

2.71828+%2B0.0536053696428=+0.7+t

t=2.7718853696428%2F0.7

t=3.9