Establishment of the power-time curve equation of bacterial growth in the log phase

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, v_i/v_i+1 = b₁+b₂v_i+2/v_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 v = 1.05(e^0.0228t-e^-0.0175t), and for V. bollisae as v = 1.58(e^0.0278t-e^-0.0170t).