Biologists stocked a lake with 160 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 4,000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years. P

Therefore logistic equation is

Step-by-step explanation:

The logistic equation is

The analytic solution is

;

P(t) = the population at time t.

K = the carrying capacity = 4,000

k= constant proportionality

t= time

= 160.

The number of fish tripled in the first year.

P(1) = 3×160 =480

=24

.....(1)

When t= 1 , P(1)=480

taking ln both sides

Putting the value of k in equation (1)

Therefore logistic equation is

x = 17

step-by-step explanation:

1st step: isolate x.

24 - 3x = -27

-24         -24

-3x   =   -51

2nd step: divide.

-3x     =   -51

  3             3

  x       =     17

hope this