Question 3 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. "What do you mean, grown?", you ask: Your computer explains that a special bacteria is grown in this laboratory. and converted into fuel. A specific amount of bacteria must be: present for the next step in the process to work (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: P(t) = 3et/ 16 Your computer continues with a note from the files that the alien civilization performed these calculations on the linearization of P (t:). Therefore; you will need to linearize P (t:) and then use that model to determine when to remove the light source to have: 3:099 million bacteria: Your linearization should be around t = 0; since this is the time when the light source is switched on. L.(t) = Using this linearization, after how many minutes (to three decimal places) will you turn off the light to generate: a population of 3:099 million bacteria? t = Number minutes Explain .imypourcowm woodess aand witthyouurcommwoot . howycouarrived atthiss reesutt. Be sureetto ceppdam use igg cad ca uss ocoronepiss too lined tes.umgod tittie wcork cofftthe gramme cutess gomtteam