The equation which describes the logarithmic phase of bacterial growth in batch culture is: Log10Nt = 0.301kt + log10N0.
a. derive the equation
2007-12-20 08:37:19 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Log10Nt = 0.301kt + log10N0
Log10Nt - log10N0 = 0.301kt
Log10(Nt/N0) = 0.301kt
Nt / N0 = 10^(0.301kt)
Nt = N0*10^(0.301kt)
2007-12-20 08:44:07 · answer #1 · answered by psbhowmick 6 · 1⤊ 1⤋
N = No10^(kt)
log N = log No10^(kt) = log No + log 10^kt
log N = log No + kt
I think you may have left out some info.
2007-12-20 16:52:55 · answer #2 · answered by ironduke8159 7 · 0⤊ 2⤋
If they want to derive the equation then you get:
dN/(N*ln10) = 0.301kdt. (because log10N = ln(N)/ln10)
therefore: dN/dt = N'(t) = 0.301k*N*ln10 = (ln10)*0.301k(10^(0.301kt + log10N0) = (ln10)*0.031kN0*10^(0.301kt)
2007-12-20 16:53:27 · answer #3 · answered by Christophe G 4 · 0⤊ 2⤋