Question

There are 10000 fishes in koorsala and the fish population obeys the logistic model with harvesting.

per capita birth rate is 14% per year

the people have been catching 400 fish per year for a long time. One year, due to new fishing equipment, the harvesting rate increases to 550 fish per year.

Assuming they carry on with this increased harvesting rate, what will be the fish population in the long run?

Give your answer correct to the nearest integer.

Answer 1

Based on the information presented above, we can summarise the following :-

1.) Current population of fishes in Koorsala = 10,000

2.) Per capita Berth Rate = 14%(This means for every fish in Koorsala, there is a change of 14% of another fish to be born)

3.) Yearly fish caught = 400

4.) Increased fish due to new harvesting technique = 550

To understand the increase in fishes using the new harvesting technique, we can use the following formula :-

(No.of fishes in the new technique - No.of fishes per the old technique) / No.of fishes per old technique

=(550 - 400) / 400

=150/400

= 37.5%

5.) Considering the current population of 10,000 fishes, we can project it for the next 8 years as follows (Note:- This calculation assumes no deaths as there is no data given on the deaths of the fishes in the year):-

The formula used as below :-

Similarly , we can project the data to any year we want in the long run by using the new percentage increase along with the current population as the base.