A lake formed by a newly constructed dam is stocked with 1,000 fish. Their population is expected to increase according to the logistic curve

N=30/(1+29e^-1.35t)
where N is the number of fish, in thousands, expected after t years. The lake will be open to fishing when the number of fish reaches 20,000. How many years, to the nearest year, will this take?

1 answer

well, just solve for t:

20 = 30/(1+29e^-1.35t)
1+29e^-1.35t = 1.5
e^-1.35t = 0.5/29
-1.35t = -4.060
t = 3