# Three cells with generation times of 30 minutes are inoculated into a culture medium. How many...

## Question:

Three cells with generation times of 30 minutes are inoculated into a culture medium. How many cells are there after 5 hours?

## Cell Division & Time:

The generation time of an individual cell, which is the average time between two consecutive cell division instances (e.g. via mitosis), is different from organism to organism. For bacteria, the generation time is called doubling time, wherein the population doubles through a specific amount of time.

Every 30 minutes, each individual cell will divide into two like-cells; therefore, through 5 hours, {eq}5\times 2 =10 {/eq} cell divisions would take place in this case. For a starting number of cells i.e. {eq}N_0 {/eq}, and with the formula for the number of cells {eq}N_n {/eq}, after {eq}n {/eq}, the number of cell divisions is given by:

$$N_n=N_0 2^n$$.

Thus, after 5 hours, the number of cells would be:

\begin{align} N_{10} &=(3) 2^{10}\\[0.2cm] N_{10} & =3(1024)\\[0.2cm] \color{blue}{N_{10}} &\color{blue}{=3,072} \end{align}.