The population of a culture of bacteria is modeled by the logistic equation P(t) = 14,250/ 1 + 29e - 0.62t . To the nearest tenth, how many days will it take the culture to reach 75% of its carrying capacity? What is the carrying capacity? What is the initial population for the model? Why a model like , p(t) = Po e^kt where Po is the initial population, would not be plausible? What are the virtues of the logistic model?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.