The doubling period of the bacteria in the culture is 3 hours.
What is exponential growth?
Exponential growth refers to a sort of function in which the growth is modelled by an exponential function. The growth of the organisms in this culture is modelled by the equation; P(t) = Poe^rt
Where;
P(t) = population at time t
Po = initial population
r = growth rate
t = time taken
Now;
208,000 = 6,500e^2.5r
208,000/ 6,500 = e^2.5r
ln(208,000/ 6,500) = ln (e^2.5r)
3.46 = 2.5 r
r = 3.46/2.5
r = 1.38 hr-1
If the population is doubled, we have 416000
416000 = 6,500e^(1.38t)
416000/6,500 = e^(1.38t)
64 = e^(1.38t)
ln(64) = lne^(1.38t)
4.15 = 1.38t
t = 4.15 / 1.38
t = 3 hours
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