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Portfolio: Creating a Logistic Model of Fish Population - Math Problem Example

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In the above math problem 'Math Portfolio: Creating a Logistic Model of Fish Population', using the formulas, a logistic model is built in stages, which reflects the increase in the conditional population of freshwater fish that developed from 10,000 individuals placed in the lake created by the hydropower project, and a hypothetical increase in the fish population is determined…
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Math Portfolio: Creating a Logistic Model of Fish Population
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Download file to see previous pages 1. A hydroelectric project is expected to create a large lake into which some fish are to be placed. A biologist estimates that if 10,000 fish were introduced into the lake, the population of fish would increase by 50% in the first year, but the long-term sustainable limit would be about 60,000. Form the information above, write two ordered pairs in the form where. Hence, determine the slope and equation of the linear growth factor in terms of u(n).
It is given that if 10,000 fish were introduced into the lake, the population of fish would increase by 50% in the first year, therefore this will be the value for ordered pair and that will be equal to. Furthermore, the long-term sustainable limit is given as 60,000, which means that at this time there will be no further population increase (for fish). Therefore, the growth rate at this particular moment will be equal to 1 (.i.e. 0% increase in fish population thereafter), which means that the second ordered pair, will be (60,000,1).
It is given that a logistic model takes the form of a Geometric model; however, the growth factor depends on the size of the population and is variable. In the case of a logistic model, the growth factor is often estimated as a linear function by taking estimates of the projected initial growth rate and the eventual population limit. Therefore, assuming growth factor (r) takes the form of a linear equation and depends upon the population of fish present at that moment (year n).
Using the logistic function model derived above, the fish population over the next 20 years is shown in below table 1. From table 1, it can be seen that from year 17th onwards, the population of fish will be equal to the sustainable limit of 60,000.
4. The biologist speculates that the initial growth rate may vary considerably. Following the process above, fine new logistic function models for using initial growth rates 2, 2.3, and 2.5. Describe any new developments. ...Download file to see next pagesRead More
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