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?

Answer 1

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

Answer 2

answer is 0.8