Growing the Raw Materials

As the gate opens, you step into a room that appears to be a laboratory of some kind. Your com you that this is where the raw materials that power the spacecraft are grown. "What do you mean, ask. Your computer explains that a special bacteria is grown in this laboratory and converte specific amount of bacteria must be present for the next step in the process to work $($within margin of error$).$ The computer provides you with information about the population of the bacteria an exponential model, shown below. In this model, $P$ is the population of bacteria $($total count, millions$)$ and $t$ is the time measured in minutes. The population will grow based on this mode source is provided and stop immediately once the light source is removed.

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

Your computer continues with a note from the files that the alien civilization performed these calcu linearization of $P(t).$ Therefore, you will need to linearize $P(t)$ and then use that model to deter remove the light source to have $5\mathrm{.}16$ million bacteria. Your linearization should be around $t=0$ the time when the light source is switched on$.$