Question

Let P(t) denote the population of bacteria in a

Petri disht hours after bacteria are introduced to the environment
of the Petri dish. Suppose that the initial population of bacteria
is known to be 5000, and that the bacteria population doubles
every 6 hours. Assume that the population can grow indefinitely.

Give a formula for P(t).

Answer 1

well, if the population is doubling from whatever they happen to be, so that means the growth rate is 100%, so if they're hmmm "g", then later they become "2g", or doubled, and the later becomes "4g" and so on, so the rate is simply 100%, because "g" plus "g" is just 2g, and "2g" plus "2g" is just 4g and so on, anyhow

`\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{(t)/(c)}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &5000\\ r=rate\to 100\%\to (100)/(100)\dotfill &1\\ t=hours\\ c=period\to &6 \end{cases} \\\\\\ A=5000(1 + 1)^{(t)/(6)}\implies A=5000(2)^{(t)/(6)}\implies {\Large \begin{array}{llll} P(t)=5000(2)^{(t)/(6)} \end{array}}`