Biosphere III

Pre-calc/Calc narrative worksheet
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  BacharachBiosphere III(MA version: omit 5,6,10-17,23)In preparation for colonization of extraterrestrial bodies, NASA has commissionedthe Biosphere project which attempts to sustain human life in a completely self-sufficient,self-contained environment. The first attempt, undertaken by Professors (Names, name,name, name, name, name), ended in a catastrophic fire when one of the composting plantsexploded from a clogged methane tube. The second Biosphere project included teammembers (Names, name, name, name, name, name). This project ended following anargument over crop rotation - half the team was for clockwise, the other half for counter-clockwise; let’s just say it got bloody before it was all over.You are one of the planners of Biosphere III, and you must solve several problemsrelated to amounts and supplies.The (p)opulation as a function of (t)ime (in days) of bacteria “O-give”, which supplyoxygen for the biosphere, increases according to the following logistics growth function: 6.5 610147 t   pe − ×=+ . This equation is derived from the differential equationdydxkyAy = − b  and has the general form ( ) 1 Akt   A y t  Be − =+ . 1At t = 0, what is the population of O-give?2At t = ∞ , what is the population of O-give?3Graph population vs. time. Use a graphing calculator to assist you find at least 12specific points.4After about how many days does the rate of increase of the bacteria begin to slow?5Using the general form of the equation, and/or the differential equation, find thetime t and y value at which the rate of increase is greatest. What is therate of increase at this point? Answers should be in terms of A, B, and k.6What is the rate of increase of the number of O-give with respect to time after 20days? after 100 days?Each O-give bacterium produces 10 molecules of oxygen every hour. Each humanrequires 5 X 10 6 molecules of O 2 every hour. There will be two human females (name and  name) and two human males (name and name) living in Biosphere III. Any produced O 2 that is not used in the following hour decays to other oxide compounds.7How many O-give bacteria are necessary to sustain the introduction of the firsthuman?8After how long would all four humans be able to live in Biosphere III?9What is the most number of humans that would be able to live in it?10Redo question 7 if produced O 2 does not decay each hour.In order to deflect the maximum amount of harsh ultraviolet rays from the sun (eventualcolonization will likely take place where there is little natural atmosphere), you must makeseveral structural considerations as to the shape of Biosphere III. You will want the proto-colony to be the shape derived from rotating the curve 2 2 1,0,02500400  x y x y + = > >  about the y-axis, where x and y are in meters and y will represent the height of your 3-Dshape. The residents of Biosphere III will need to plant fruit trees. Orange trees willgrow to a height of 10 meters. Apple trees will grow to a height of 5 meters, and coconut palms will reach 18 meters.11If the polysilica-carbonaceous material of the dome costs $250 per square meter,what will be the total cost of the structure?12What percentage of the ground on Biosphere III is available for planting orangetrees? Apple trees? Coconut palms?13What will the total volume of the proto-colony be?14If, through the special filter in the material of Biosphere III, harmful ultravioletlight is deflected at incident angles between 15 ° and 35 ° , how much area can bedevoted to outside recreation at noon?The humans in Biosphere III, tired of getting hit by falling coconuts, disregard NASAorders and plant only apple and orange trees. Each apple tree requires 10 m 2 , and eachorange tree requires 20m 2 . Each produces 60 fruits and 40 fruits, respectively.15How much area can be planted with apple trees but not orange trees?16How much area can be planted with both types?  17How many trees of each type should be planted in order to produce the most fruit?How much fruit will that be? NASA funding is cut drastically. Biosphere III is no longer monitored actively. The GreatRevolution of (current year) takes place as math students from all nations unite to takeover the world. This insurrection is led by “Che” (name), “Fidel” (name), (name)“Franco”, and “Mao-Tse” (name). Some years later Biosphere III and one of its longdead inhabitants (name) is discovered.18If (name’s) body had had 90% as much C 14 as a live body would, how long agowould (he/she) have died?19How many years would it take for the amount in her body to drop to 5% (theamount when she was actually found)?It is believed that the srcinal colonists had many generations of descendants. Recordsindicate that the youngest inhabitant (name) was 1000 years the junior of the person in the previous question. They lived the same number of years.20What C 14 percentage should be in (name’s) body?The (current year) Revolution went too far. Students, (names), drunk with power, beganto burn all math books. The fire began over three acres and spread exponentiallyaccording to the equation: Area = (Original area)(1.1) (2 x number of days) 21How long before the fire had quadrupled in size?22How long before the fire had burned 1000 acres?23How fast were the flames enveloping the landscape after 10 days?Heat was given off by the flames according to the following equation:Temperature ( ° F) = 30[log 4 (w/d) 3 ], where ‘w’ is wind speed in meters/second and ‘d’ isdistance in kilometers from the flames.24Rewrite the equation into natural logs using change-of-base and logarithm laws.25If the wind was blowing at 20m/s and you were 30m from the inferno, what wouldthe temperature have been?  26If the temperature was 300 ° F and you were 50m from the fire, what was the windspeed?As I’m sure you know, the planning you have undertaken is far more simplistic than would be necessary to actually make such a proto-colony successful (such as the previous,flawed attempts).27List, in complete sentences, 5 problems with restricting your planning to only theconditions given in the previous questions.

Relatório 09

Aug 16, 2017


Aug 16, 2017
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