Chapter 12: Growth and decay – Exponents and logarithms

In biology (and every other discipline in science) you will often have to deal with numbers which vary in magnitude to an extraordinary degree. Often the only way to graphically represent such data is to use logarithmic or exponential scales and you will find that you often need to interpret this kind of data. Related to this, there are many important measurements which use an exponential scale (e.g. pH). Moreover, many relationships between variables are best described by exponential functions. For example, in a growing bacterial or cancerous cell population, the number of cells can increase exponentially over time or the clearance of a drug from your body can decrease exponentially over time. Being able to work with logarithms and exponents to describe such relationships is fundamental to understanding them and allows us to make accurate predictions.

The spread of infectious diseases can often also be described by exponential functions and these are certain to be a part of any mathematical modelling of their epidemiology (studying the distribution, risk factors and spread in the community). It is of vital importance in managing infectious disease that we are able to understand how it is likely to spread in the community, to know the risk factors involved and to predict the effects of any interventions we might implement.

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