A logistic model

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IB Mathematics HL Type II Portfolio: Creating a logistic model International School of Helsingborg - Christian Jorgensen

Creating a logistic model

Christian Jorgensen

IB Diploma Programme

IB Mathematics HL Portfolio type 2

Candidate number

International School of Helsingborg, Sweden

1

IB Mathematics HL Type II Portfolio: Creating a logistic model International School of Helsingborg - Christian Jorgensen

Theory

A logistic model is expressed as:

un?1 ? run

{1}

The growth factor r varies according to un. If r=1 then the population is stable.

Solution

1. A hydroelectric project is expected to create a large lake into which some fish are to be placed. A biologist estimates that if 1x104 fish were introduced into the lake, the population of fish would increase by 50% in the first year, but the long-term sustainability limit would be about 6 x104. From the information above, write two ordered pairs in the form (u0, r0), (u0, r0) where Un=6x104. Hence, determine the slope and equation of the linear growth in terms of Un

As Un =6 ?104 , the population in the lake is stable. Thus from the