Question

In milk, at ${37}^{o}C$, lactobacillus acidophilus is a generation time of about $75$ minutes. Calculate the population relative to the initial value at $30,60,75,90$ and $150$ minutes.

Answer 1

For growth kinetics,
$k=-\frac{2.303}{t}{\log }_{10}\left(\frac{a}{a+x}\right)$
$k=-\frac{2.303}{t}{\log }_{10}\left(\frac{N_0}{N}\right)$
Generation time $=75$ minutes; $a=1$, $a+x=2$
$k=-\frac{2.303}{75}{\log }_{10}\left(\frac{1}{1+1}\right)=0.00924{min}^{-1}$
After $30$ minutes,
$k=\frac{-2.303}{t}{\log }_{10}\left(\frac{N_0}{N}\right)$
$0.00924=-\frac{2.303}{30}{\log }_{10}\left(\frac{N_0}{N}\right)$
$\frac{N}{N_0}=1.319\approx 1.32$
Similarly, we may calculate after $60,75,90$ and $150$ minutes.