Lecture 20 — Doubling Time and Decimal Reduction Time

What is doubling time?

The time required for a bacterial population to double during exponential growth.

How do you calculate the number of generations?

n = elapsed time ÷ doubling time.

How do you calculate final cell number during exponential growth?

N = N0 × 2^(time/doubling time).

What is decimal reduction time (D-value)?

The time required under specified conditions to reduce the viable population by 90%, or one power of ten.

How many cells remain after one D-value?

10% of the original viable population.

How many cells remain after three D-values?

0.1% of the original population; divide the original count by 1,000.

How do you calculate viable cells after a given disinfection time?

N = N0 × 10^(-time/D).

A population starts at 10^7 cells and D = 4 minutes. How many survive after 12 minutes?

10^4 viable cells; 12/4 = 3 decimal reductions.

How is a logarithmic axis different from a linear axis?

Each equal vertical step represents multiplication by a constant factor (often 10), rather than addition of a constant.

How can doubling time be read from a growth graph?

Find two points where population doubles and subtract their times.

How can decimal reduction time be read from a death graph?

Find the time between two viable counts differing by a factor of 10.

Why are logarithmic graphs useful for bacterial populations?

They display many orders of magnitude and make exponential growth or log death appear as straight lines.