In an ecosystem with unlimited resources and no predators, the population of a species would be expected to grow exponentially. This means that the graph of population versus time would be characterized by a J-shaped curve.
Initially, the population would increase slowly as individuals reproduce. However, as the population grows, the rate of reproduction would increase, leading to more rapid population growth. Over time, this results in a steep upward slope in the graph, reflecting the exponential growth pattern.
In mathematical terms, this can often be represented by the equation \( P(t) = P_0 e^{rt} \), where \( P(t) \) is the population at time \( t \), \( P_0 \) is the initial population size, \( r \) is the intrinsic growth rate, and \( e \) is the base of the natural logarithm.
In summary, under the conditions you've specified, the shape of the population versus time graph would be a J-shaped curve indicating exponential growth.
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