Question

Biologists stock a lake with 160

Answer 1

Answer:

$P ( t ) = \frac{9100.024}{1 + 55.875e^-^1^.^1^3^5^0^6^*^t}$

Step-by-step explanation:

Solution:-

- We are given a logistic growth model of the fish population cultured. The logistic growth of fish population is modeled by the following equation:

                         $P ( t ) = \frac{c}{1 + 55.875e^-^ 1^.^1^3^5^0^6^t}$

Where,        c: the constant to be evaluated.

- We are given the initial conditions for the model where at t = 0. The initial population was given to be:

t = 0 ,              Po = 160

                       N ( carrying capacity ) = 9100

- After a year, t = 1. The population was tripled from the initial value. That is P ( 1 ) = Po*3 = 160*3 = 480.

- We will use the given logistic model and set P ( 1 ) = 480 and determine the constant ( c ) as follows:

                           $P ( 1 ) = \frac{c}{1 + 55.875e^-^ 1^.^1^3^5^0^6^*^1} = 480\\\\c = 480* [ 1 + 55.875e^-^ 1^.^1^3^5^0^6]\\\\c = 9100.024$

- The complete model can be written as:

                            $P ( t ) = \frac{9100.024}{1 + 55.875e^-^1^.^1^3^5^0^6^*^t}$