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a bacteria culture starts with 260 bacteria and grows at a rate proportional to

its size after 5 hours there will be 1300 bacteria express the population after t hours as a function of t

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  1. dp/dt = kp
    dp/p = k dt
    lnp = kt+c
    p = c*e^(kt)
    since p(0) = 260, c = 260 and
    p = 260 e^(kt)
    To find k, solve
    260 e^(5k) = 1300

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