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The population of a colony of bacteria is modeled by the function p(x)=50(e^-x - e^-x^2)+10 , for 0 ≤ x, where population P is in thousands, x is in hours, and x = 0 corresponds to the moment of introduction of a certain chemical into the colony's environment. At which time below is the rate of population growth the greatest?

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2 answers

  1. answer is 0.8

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  2. you want to find where p'(x) has a max

    p' = 50(2x e^-x^2 - e^-x)

    See http://www.wolframalpha.com/input/?i=2x+e^-x^2+-+e^-x

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