Establishment of The Power—Time Curve Equation of Bacterial Growth in the Log Phase

Abstract

The power-time curves of two species of bacteria, Vibro metschnikovii, Vibro bollisae were determined calorimetrically by using a 2277 bioactivity monitor. The power-time curve equation of bacterial growth in the log phase can be expressed as

$$v = A(e^{k_1 t} - e^{ - kt} )$$

. A self-function recursion equation, f_i=b₁f_i+1+b₂f_i+2, was obtained through the perfect non-linear function

$$f(t) = A + Be^{ - k_1 t} + Ce^{ - k_2 t} $$

. A linear equation, ν_i/ν_i+1=b₁+b₂ν_i+2/ν_i+1, was obtained by using the self-function recursion equation. The rate constants of bacterial growth k₁, the time constant of the calorimeter k, the generation times G, and the pre-exponential factors A were obtained from the power—time curve equations.

Power—time curve equations of bacterial growth in the log phase are expressed for V.metschnikovii as ν=1.05(e^0.0228t−e^−0.0175t), and for V. bollisae as ν=1.58(e^0.0278t−e^−0.0170t).