Question

The number of bacteria in a certain culture doubles every hour. If there were $30$ bacteria present in the culture initially, how many bacteria will be present at the end of ${14}^{th}$ hour?

Answer 1

The number of bacteria present initially, $a=30$

The rate at which bacteria increases every hour, $r=2$

The number of bacteria at the end of the first hour $=ar=30\left(2\right)$

The number of bacteria at the end of second hour $=a{r}^2=30{\left(2\right)}^2$

The number of bacteria at the end of $n^{th}$ hour $=a{r}^n=30{\left(2\right)}^n$

Bacteria at the end of ${14}^{th}$ hour $=30{\left(2\right)}^{14}$