Question

You decided to become a super cool food scientist and upon graduation, was hired at an ice cream company. The first product you are asked to work on is soft-serve ice cream. Soft-serve ice cream starts off as a liquid ice cream mix that will later be frozen into delicious, smooth and creamy ice cream. Your lab mate was showing you how to make the liquid ice cream mix, and after making it, forgot to put it in the refrigerator before heading home. Unfortunately, that ice cream mix contained 2 viable food infection type microorganisms. If the average lag phase generation time is 105 minutes, the average log phase generation time is 35 minutes, and three generation times (16 microorganisms) are required for the system to switch from the lag to the log phase, how many microorganisms would be present in the mix when you returned to the lab 14 hours later. Please provide your answer to the nearest whole number

Answer 1

First, you need to know that microorganisms' growth in a culture can be described with the following equation:

= Number of microorganisms at time t

= Number of initial microorganisms.

= the number of generations in time t

We solve for :   

And    where k is the mean rate growth constant.(it's 1 generation/35min, we figure it out thanks to the duration of lag phase)

We also know that where g is the mean generation time

We now use the equation to get the number of divisions that occur in those 14 hours and substitute the values in the original equation.

During the 14 hours that the ice cream is left out of the fridge occurred 24 divisions that account for 268435456 microorganisms (assuming there are enough resources so they don't go on stationary phase)