The rate of bacterial cell decline in the death phase follows:
Decline phase marks period when lethal environmental stresses exceed capacity to repair damage and maintain homeostasis, leading to net loss of viability. Population decay is often well described by exponential decay mathematically analogous to radioactive decay, reflecting stochastic individual death. First-order kinetics states instantaneous rate of viable cell loss is directly proportional to number of viable cells present at that instant expressed as dN/dt equals minus kd times N where kd is first-order death rate constant per time. Integration from time zero yields ln Nt equals ln N0 minu
Ref: Lodish et al., Molecular Cell Biology, 8th ed., Chapter 4: Death Phase and First-Order Kinetics Model.