PctoredlestQuestionsheet

Growing the Raw Materials

As the gate opens. you step inlo a room that appears to be a baboratory of some kind Your completer intoms you that the is where the raw makriats that power the spacecraf are grown What do you mean, grownte, you ask. Your computer explains that a specid bacteria is gown in this laboratory and corverted into fuel. A speonc amount of backeria must be presemt for the nest sep in the process to wotk $($within a neasonatle an exponental moded, stown beiow in this moded, $P$ a the population of bacteria folal count, measured in millors$)$ and $t$ is the time measured in mathes The pepuation wil grow hasod on this model once a light

$P(t)=5e^{\frac{t}{16}}$

Inearization of $P(t).$ Therefore, you wil reed to areave $P(t)$ and ihen use thas model to determine when to remove the aght source so have $5\mathrm{.}155$ milon baclema youriheanzances shoils be around $t-0,$ shce this is the sme when the lath source is suncted on$.$

$$ a poputation of $5\mathrm{.}155$ millon bacterta?

$t=$ minutes