Question

suppose a single bacterium is placed in a bottle at 11 a.m. It grows at 11:01 and divides into two bactrim. These two bactrim each grow and at 1102 divided into 4 which grow and at 1103 divided into 8 and so on. Now supposed to bactrim continue to double every minute and the bottle is full at 12 how many bactrim will there be at 11:42

Answer 1

now, the bacterium is doubling every minute.

that means, for every minute, it has a "rate of growth" of 100%, is just growing by 100% of whatever the current value is, or just doubling.

we also know that the initial value was just 1 bacterium, how many will there be in 42 minutes? namely at 11:42am.


`\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &1\\ r=rate\to 100\%\to (100)/(100)\to &1.00\\ t=\textit{elapsed time}\to &42\\ \end{cases} \\\\\\ A=1(1+1.00)^(42)\implies A=1(2)^(42)\implies A=2^(42)`