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

Maths - Essay Example 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 . It is also given that the long-term sustainable limit of population of fish is 60,000. This will be case 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 similar form as the geometric population growth model. However, in this case, the growth factor depends on the size of the population and is variable. In previous section 1, the equation of growth factor (r) is determined, which is: 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. 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 correctly determine the population of the fish over the 20 years period. For example, for initial growth rate of 2, the fish population exceeds stable 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) ten 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