Reproducibility from one day to the next and between different laboratories is necessary before meaningful measurements can be made on growing cells.

**Exponentially Growing Populations**

Reproducibility
from one day to the next and between different laboratories is necessary
before meaningful measurements can be made on growing cells. Populations of
cells that are not overcrowded or limited by oxygen, nutrients, or ions grow
freely and can be easily reproduced. Such freely growing populations are almost
universally used in molecular biology, and several of their properties are
important. The rate of increase in the number of cells in a freely growing
population is proportional to the number of cells present, that is,

In these
expressions µ is
termed the exponential growth rate of the cells. The following properties of
the exponential function are frequently useful when manipulating data or
expressions involving growth of cells.

Quantities
growing with the population increase as e^{µ}^{t}_{.}
Throughout this book we will use µ as the
exponential growth rate. The time required for cells to double in number, *T _{d},* is easier to measure
experimentally as well as to think about than the exponential growth rate.
Therefore we often need to interconvert the two rates

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