Number of bacteria present in a culture at any time, t hours, is modelled by the equation N=ne^kt If the original number is doubled in 3 hours find k?
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The number of bacteria in a culture after a duration of time t is given by the equation `N = n*e^(k*t)` where n is the initial number of bacteria.
As the number of bacteria becomes double in 3 hours, the resulting equation is: `2*n = n*e^(k*3)`
=> `2 = e^(k*3)`
take the natural log of both the sides
=> `ln 2 = 3*k*ln e`
=> `ln 2 = 3*k`
=> `k = (ln 2)/3`
=> `k ~~ 0.2310`
The value of k is approximately 0.2310
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