Question

A certain kind of bacteria growing on your kitchen counter doubles every 30 mins.. Assuming that you start with only one bacterium, how many bacteria could be present at the end of 180 mins.

Answer 1

$\bf \textit{Periodic Exponential Growth}\\\\ A=I(1 + r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &1\\ r=rate\to 100\%\to \frac{100}{100}\to &1.00\\ t=\textit{elapsed time}\to &180\\ p=period\to &30 \end{cases} \\\\\\ A=1(1 + 1)^{\frac{180}{30}}$

Answer 2

What you can do is start with the key details in it... the main ones are that the bacteria grows every 30 minutes, you start with 1 bacteria, and the end time is 180 minutes. Basically you know that 3 goes into 18 6 times so 30 goes into 180 6 times which means that if you started with 1 bacteria you will end up with 7. Understand?