can someone show me how to get to the anwser of this function using the pert formula???

Question

a small lake is stacked with a certain amount of a species of fish. Their population is modedled by the function p=10/1+4e^-.8t where p is the number of fish in thousands, and t is measured in years since the lake was stocked.
Find the fish population after 5 years????
Once the fish population reaches 8000 after how many years?????

Answer 1

Hi,
After five years:
p=10/[1+4e^(-.8t)]
p=10/[1+4e^(-.8*5)]
Plug that into your calculator and you'll get:
9.31738...
So, it's about 9317 fishes.
To get the years for 8000 fishes, we need to solve for t.
8=10/[1+4e^(-.8*t)]
1+4e^(-.8*t) =10/8
4e^(-.8*t)=10/8-8/8
e^(-.8*t)= 1/4/4
ln(e^(-.8*t))= ln(1/16)
-.8t = ln(1/16)
t = ln(1/16)/(-.8)
t = 3.4657.... years

FE