Growing the Raw Materials As the gate opens. you step into a room that appears to be a laboratory of some kind. Your computer informs you that this is where the raw materials that power the spacecraft are grown. "Yiihat do you mean. grown'i". you ask. Your computer explains that a special bacteria is grown in this laboratory and converted into fuel. A specic amount of bacteria must be present for the next step in the process to wort: [within a reasonable margin of error}. The computer provides you with information about the population of the bacteria, which follow an exponential model, shown below. In this model, P is the population of bacteria [total count, measured in millions} and t is the time measured in minutes. The population will grow based on this model once a light source is provided and stop immediately once the light source is removed. Pit] = setr'd Your computer continues with a note from the files that the alien civilization performed these calculations on the linearization of F it}. Therefore. you will need to linearize F {t} and then use that model to determine when to remove the light source to have 3.081 million bacteria. Your linearization should be around it = I}. since this is the time when the light source is switch ed on. at % VIE lel 1r 5'11: [u] Lit} = b Using this linearization, after how many minutes [to three decimal places} will you turn off the light to generate a population of 3.031 million bacteria