Projected Cell Count from Doubling Time
The inverse of the doubling-time tile: the projected count (or OD) from a known doubling time over an elapsed time, N = N0 x 2^(t / Td), with the doublings t/Td and the fold increase 2^(t/Td). 100,000 cells at an 8 h doubling time reach 800,000 in 24 h (3 doublings, 8x). Holds only in log phase; the projection over-predicts once the culture nears stationary phase. The culture and conditions govern.
Formula and source
N = N0 x 2^(elapsed / Td), the inverse of Td = elapsed x ln(2) / ln(N / N0); doublings = elapsed / Td; fold_increase = 2^(elapsed / Td).
Exponential-growth / population-doubling kinetics (standard growth analysis), solved for the projected count, by name.
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