When placed in favourable conditions populations of bacteria can increase at remarkable rates, given that each division gives rise to two identical daughter cells, then each has the potential to divide again.

**POPULATION GROWTH**

When placed in
favourable conditions populations of bacteria can increase at remarkable rates,
given that each division gives rise to two identical daughter cells, then each
has the potential to divide again. Thus cell numbers will increase
exponentially as a function of time. For a microorganism growing with a
generation time of 20 minutes, one cell will have divided three times within an
hour to give a total of eight cells. After 20 hours of continued division at
this rate then the accumulated mass of bacterial cells would be approximately
70 kg (the weight of an average man). Ten hours later the mass would be
equivalent to the combined body weight of the entire population of the UK.
Clearly this does not happen in nature; rather, the supply of nutrients becomes
exhausted and the organisms grow considerably more slowly, if at all.

The time interval between
one cell division and the next is called the *generation time*. When considering a growing culture containing
thousands of cells, a mean generation time is usually calculated. As one cell
doubles to become two cells, which then multiply to become four cells and so
on, the number of bacteria *n* in any
generation can be expressed as:

1st generation n = 1 × 2
= 2 ^{1}

2nd generation n = 1 × 2
× 2 = 2 ^{2}

3rd generation n = 1 × 2
× 2 × 2 = 2 ^{2}

x th generation n = 1 ×
2 ^{x} = 2 ^{x}

For an initial
population of *N*_{o} cells, as
distinct from one cell, at the *x*th
generation the cell population will be:

N= *N*_{o} × 2^{x}

where *N* is the final cell number, *N*_{o} the initial cell number
and *x* the number of generations. To
express this equation in terms of *x*,
then:

log *N* = log *N*_{o} + *x* log
2

log *N* − log *N*_{o} = *x* log
2

*x *=* *(log* N *−* *log* N*_{o}* *)/ log 2* *=* *(log* N *−* *log* N*_{o}* *)/0.301

.

= 3.3(log *N* − log *N*_{o} )

The actual generation
time is calculated by dividing *x* into
*t* where *t* represents the hours or minutes of exponential growth.

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