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The exponential population growth represents the population increase under an ideal condition, resulting in a J-shaped growth curve plotted over time. It is different from the S-shape that the logistic population growth illustrates. On the contrary, with the limitations of food supply, predators and other environmental factors, the logistic population growth model modifies the changes of the growth rate as the population size reaches the carrying capacity, which is symbolized by K, meaning the maximum population size that a particular environment is able to maintain (Campbell and Reece 2011). The per capita rate of increase is the difference between the per capita birth rate, “the number of offspring produced per unit time by an average member of population”, and the per capita death rate, the number of deaths per individual per unit time (Campbell and Reece 2011). It implies the population will increase as the per capita rate of increase, r, is larger than zero, which in turn, shows that a negative r will lead to the decrease of the population. Unlike in the logistic population growth, the per capita rate of increase goes to zero while it is at the carrying capacity, the per capita rate of increase is maximized for the exponential population

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At the beginning in the acceleration phase, the birth rate surpasses the death rate, then it turns into deceleration phase where the death rate roughly equals to the birth rate through the inflection point, a point that the growth rate is constant. At equilibrium, the steady state occurs that the birth rate and the death rate are equal. The growth of the Paramecium caudatum and Paramecium aurelia in separate media should fit the logistic population