Question

A colony of bacteria starts with 2 bacteria at noon if the number of bacteria triples every 30 minutes, how many bacteria will be present at 3:00 pm on the same day?

A 446
B 729
C 1,458
D 46,656
E 118,098

Please HELP and show your work if you decide to answer! Thank-you!

Answer 1

if the colony is tripling every 30mins, that simply means is "increasing at a rate of 200%", so, whatever the current is, plus 200% of that, which makes it 300% or a tripling rate

now, from noon to 3pm, there are 6 half-hours, so it has gone through that cycle 6 times already, or 6 periods


`\bf \qquad \textit{Amount for Exponential change}\\\\ A=P(1\pm r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{starting amount}\to &2\\ r=rate\to 200\%\to (200)/(100)\to &2.00\\ t=\textit{elapsed period}\to &6\\ \end{cases} \\\\\\ A=2(1+2.00)^6`