Maths Essay Example | Topics and Well Written Essays - 2500 words

Maths - Essay Example1. A hydroelectric project is expected to create a large lake into which some seek are to be placed. A biologist estimates that if 10,000 fish were introduced into the lake, the state of fish would increase by 50% in the initial 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 emergence factor in terms of .It is also given that the long-term sustainable limit of people of fish is 60,000. This will be cheek when there is no increase in fish for next year, therefore, the growth factor (r) for this case will be equal to 1.Since, a logistic population growth model takes a connatural form as the geometric population growth model. However, in this case, the growth factor depends on the coat of the population and is variable. In previous section 1, the equation of growth factor (r) is determined, which is4. The biologist speculates that the initial growth rate may vary considerably. Following the process above, fine new logistic function models for utilise initial growth rates 2, 2.3, and 2.5. Describe any new developments.From table 2 data, it can be seen that for higher values of initial growth rate r (2, 2.3, 2.5 and 2.9), the logistic model does not aright determine the population of the fish over the 20 years period. For example, for initial growth rate of 2, the fish population exceeds constant population (60,000) three times for initial growth rate of 2.3, the fish population exceeds stable population (60,000) eight times and for initial growth rate of 2.5, the fish population exceeds stable population (60,000) nine times. For initial growth rate of 2.9, the fish population exceeds stable population (60,000) ex times and sometimes it touches the population value of approximately 70,000.For initial growth rate of 2.9, the fish population exceeds stable population (60,000) ten times