Question

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
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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