Question

Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1500 fish. Absent constraints, the population would grow by 170% per year.
If the starting population is given by p0 = 400, then after one breeding season the population of the pond is given by p1 =.
After two breeding seasons the population of the pond is given by p2 =.

Answer 1

Answer:

The correct answer is  p1 = 898 and p2 = 1020.

Explanation:

This is a logistic growth problem and will utilize the following formula:  

$Pn = P_{n-1} + r (1- \frac{P_{n-1} }{k} ) P_{n-1}$

Given ;

r = 1.7

k = 1500

Po = 400

then,

$Pn = 400 + 1.7 (1- \frac{400 }{1500} ) 400$

= 400 + 1.7 (293)

= 400+ 498

P₁= 898

Similarly,

$P₂= P_{2-1} + r (1- \frac{P_{2-1} }{k} ) P_{2-1}$

= $Pn = 400 + 1.7 (1- \frac{898 }{1500} ) 400$

= 1020

Thus, the correct answer is  p1 = 898 and p2 = 1020.