Practice question

Binary fission results in population doubling each generation, so cell numbers after n generations follow Nt equals N0 multiplied by two raised to power n assuming synchronous division and negligible death during exponential phase. Starting inoculum N0 serves as baseline, exponent reflects geometric progression illustrating rapid amplification: single cell becomes 1024 after ten generations, over one million after twenty. For instance starting with 200 cells, sequence after successive doublings is 400 after first, 800 after second, 1600 after third, 3200 after fourth, 6400 after fifth where each interval equals one generation time under optimal conditions. Relationship underlies estimation of titers in starter cultures for dairy fermentation, prediction of final biomass in fermentors and back-calculation of generation time from plate counts. Practical deviations arise from clumping causing underestimate, filamentous growth without septation or presence of nonviable cells. While dataset lists 3200 corresponding mathematically to four doublings, fundamental equation remains Nt equals N0 times two to power generations embodying exponential increase characteristic of logarithmic phase and forming basis of quantitative microbiology and growth yield calculations.