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Posted 2 months ago
Name the growth pattern demostrated in a growing population and explain why the population can
/can not continue with this growth pattern forever
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Answer from Sia
Posted 2 months ago
The growth pattern demonstrated in a growing population is typically an exponential growth pattern. However, this population cannot continue with this growth pattern forever due to limiting factors such as resource availability, predation, disease, and environmental conditions.
Exponential Growth: In the initial stages, populations often grow exponentially, where the growth rate is proportional to the current population size. This can be represented by the equation N(t)=N0ertN(t) = N_0 e^{rt}, where N(t)N(t) is the population size at time tt, N0N_0 is the initial population size, rr is the intrinsic growth rate, and ee is the base of the natural logarithm
Limiting Factors: Exponential growth cannot continue indefinitely because resources such as food, water, and space become limited. Additionally, factors like predation, disease, and competition also play a role in slowing down population growth
Logistic Growth: As resources become limited, the population growth rate slows down and eventually stabilizes, leading to a logistic growth pattern. This can be represented by the logistic growth equation N(t)=KN0ertK+N0(ert1)N(t) = \frac{K N_0 e^{rt}}{K + N_0 (e^{rt} - 1)}, where KK is the carrying capacity of the environment
Key Concept
Exponential and Logistic Growth
Populations initially grow exponentially but cannot sustain this growth due to limiting factors, leading to a logistic growth pattern where the population stabilizes at the carrying capacity.

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