Question

A certain species of bacteria in a laboratory culture begins with 50 cells and doubles in number every 30 minutes. Write a function

fix) to model the situation where x is the number of 30-minute time periods.

Answer 1

since we know the number is doubling, so if say it was "x" right now so 30 minutes later will be "x" + 100 of "x", namely 2x, so that simply means the rate of growth is 100%.

`\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{(t)/(c)}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 100\%\to (100)/(100)\dotfill &1.00\\ t=minutes\\ c=period \dotfill &30 \end{cases} \\\\\\ A=P(1 + 1.00)^{(t)/(30)}\implies A=P(2)^{(t)/(30)}\hspace{5em}f(x)=P(2)^{(x)/(30)}`