Assignment 1: Exponential Growth In Module 4 You Were Introd

Assignment 1 Exponential Growthinmodule 4 You Were Introduced To The

In this assignment, I analyzed the exponential growth of a chosen biological population, utilizing Microsoft Excel and theoretical calculations to understand how populations expand over time under varying growth rates. The population selected for this study was a microbial culture, which allowed for manageable growth simulation within laboratory settings.

The initial population size was set at 1,000 microorganisms. Three different positive annual growth rates were chosen: 0.02 (2%), 0.04 (4%), and 0.06 (6%), with each rate differing by 2%. The time intervals selected were 10, 20, and 30 years, providing a broad view of population trajectories over moderate periods. Using the exponential growth model, the future population sizes were calculated with the formula: Future value = Present value * exp(rt), where 'r' is the growth rate, 't' is time in years, and exp is the exponential function based on the mathematical constant 'e'.

Calculations showed that at a 2% growth rate, the population increased to approximately 1,221 after 10 years, 1,491 after 20 years, and 1,821 after 30 years. At 4%, the populations were 1,491, 2,225, and 3,321 for the same respective time frames. The 6% rate resulted in significantly higher growth: about 1,822, 2,995, and 4,953 at 10, 20, and 30 years, respectively. These calculations demonstrated the nonlinear, accelerating nature of exponential growth, which was visually represented through graphing the data series in Excel. The graphs displayed curved lines, characteristic of exponential functions, with steeper slopes at higher growth rates over time.

The shape of these curves indicated that small percentage differences in growth rates could lead to substantial divergence in population size over extended periods. This nonlinear growth emphasizes the potential for rapid resource consumption if unchecked, raising concerns about environmental sustainability. In natural settings, environmental factors such as food availability, predation, disease, and habitat limitations prevent long-term exponential growth. These factors generate bottlenecks, causing populations to stabilize or decline after periods of exponential increase, indicating that unlimited growth is unrealistic in real ecosystems.

Long-term exponential growth is therefore an idealized model. In reality, populations tend to follow logistic or other growth models where growth rates diminish as resources become scarce. The implications for resource use are significant: unchecked exponential expansion could lead to overexploitation of environmental resources, habitat degradation, and biodiversity loss. Consequently, while the exponential model provides valuable insights into potential growth trends, it must be tempered with ecological constraints to accurately predict long-term population dynamics.

References

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