Question 3 0 point 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 convened 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) : 7615/2 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 7.189 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 7.189 million bacteria? 35 : Number minutes Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team. :33: IEIEIIEQEE I:=:s:= E E Q Salim A' 0' L B I Q 5 X: XE Words: 0 A Question 5 0 point Number Help Constructing the Fuel Tank "Great, I've got the fuel, but how do | get it to a spacecraft? Computer, how do | transport this fuel?" Your computer responds that the burning of the fuel destroys the container that it is held in, and that a new container is constructed for each launch of the spacecraft. The shape of the container is a cylinder with a hemisphere attached to the bottom. Your computer is able to generate an image (not to scale) and equations for the volume and surface area of this shape. You see a warning notice that supplies of materials for constructing this container are low. In order to create the container with limited supplies, you will need to provide the height and radius (to 2 decimal places) that minimizes the surface area of the container. What values do you provide? Total Volume of Fuel: 197r Equation for Volume of this Container: V : 1rr2 (h + gr) Equation for the Surface Area of this Container: 5' : 27rr'h + 37r7'2 Radius: Number Height: \"Number I Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team. ;n '3: 4- [stars 0. ;: :: 42512 :=