### Growth Curve of LPlantarum Bacteria

## by Aryn Plas

Submitted : Spring 2012

Due to bacteria’s exponential growth, the logarithm of the relative population size [y=lnN/N0] is plotted against time. There are 3 phases of the growth curve: the maximum specific growth rate mu(m), defined as the tangent in the inflection point; lag time (t_{L}), defined as the x-axis intercept of the tangent; and the asymptote (A=ln(N(infinity)/N0), the maximum value reached (Zwietering 1876). The values given in the problem statement were entered into an Excel spreadsheet and the Richards equation (ln(N/N0)=a(1+vexp(k(tau-t)))xp(-1/v) was fitted to these values. First, a guess was made for the unknown variables and the error squared was calculated. The Excel Solver tool was then used to adjust the error squared to make the unknown variable values as accurate as possible. The Richards equation was then manipulated as described in the “3 phases of the growth curve” to find maximum growth rate, lag time, and the maximum value reached.

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