MHB Logistic model/initial value problem

[ineedhelpnow]

http://www.math.upenn.edu/~zhentao/math114/sol2.pdf

for number two (click the link), can someone explain how the step where they solved for $e^{-k}$

 

[MarkFL]

The number of fish tripled in the first year, hence:

$$P(1)=1200=\frac{10000}{1+24e^{-k}}$$

$$3=\frac{25}{1+24e^{-k}}$$

$$3\left(1+24e^{-k}\right)=25$$

$$3+72e^{-k}=25$$

$$72e^{-k}=22$$

$$36e^{-k}=11$$

$$e^{-k}=\frac{11}{36}$$

 

[ineedhelpnow]

1200? that's because the number tripled right?

 

[MarkFL]

1200? that's because the number tripled right?

Yes, the initial population was 400 so after one year there would be 1200 if it tripled during that time. :D