Most populations in nature grow and decline depending on various factors such as

Question

Most populations in nature grow and decline depending on various factors such as food supply, size of habitat, predators, etc. Generally the population of a species in the future will be dependent on the population now.  Consider an independent variable x which describes the population as a fraction.  Thus a value of 0 would be extinction and a value of 1 would be the greatest conceivable population.  Then let f(x) be the fraction of population one generation later which depends on x(population now.)  Thus f(x) varies jointly with x and the room for growth 1-x.  Write an equation for the population f(x) using k as the constant of variation.  I'm stuck from the very beginning.  I don't know where to begin....

Explanation / Answer

f(x)=kx(1-x) is what f(x) varies jointly with x and 1-x means. The problem stated the constant of variation is k whichallows th equal sign.

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