Experimental data for the growth of Lactobacillus plantarum bacteria have been obtained over time, creating the need for mathematical means to model this data. We use the Gompertz model because it is a sigmoid function for a time series, where growth is slowest at the start and end of a time period. The Gompertz model is especially useful because it defines specific parameters that characterize the S-shaped curve. In addition, the Gompertz model uses relative growth, which is the logarithm of the given population compared to the initial population. This reflects the fact that bacteria grow exponentially. The important parameters that were found were the lag time and the asymptote.
"Using Calculus to Model the Growth of L. Plantarum Bacteria,"
Undergraduate Journal of Mathematical Modeling: One + Two:
2, Article 2.
DOI: http://dx.doi.org/10.5038/2326-3622.214.171.124 Available at: http://scholarcommons.usf.edu/ujmm/vol1/iss2/2
Arcadii Grinshpan, Mathematics and Statistics
Scott Campbell, Chemical & Biomedical Engineering