12. {16 points] The weight of a certain extraterrestrial creature increases at a rate pro portional to its weight. A researcher found such a creature...

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12. {16 points] The weight of a certain extraterrestrial creature increases at a rate pro—portional to its weight. A researcher found such a creature at 9am on Monday morn—ing. The researcher weighed the creature at 1Siam on Tuesday morningI and found itweighed 50g. The researcher weighed the creature again at 1Ei'pn'l on Thursday eveningI and found it weighed lfiflg. How much did the creature weigh when the researcher found it? Express your answeras single fractionI without any exponentials or logarithms. 1f}. [2!] points] The temperature of a glass is measured to he 2?” C at 9 pm and 26° Can hour later. The glass is in an air-conditioned room where the temperature is heldconstant at 2B“ C. The glam was removed flom the dishwasher at a temperature of3?” C. You may use the fact that the temperature T (in degrees lCelsius) will obey theequation To) = A + Be‘“, where t represents the number of hours after 9 pm. (a) Using the fact that in the long run, the temperature of the glass approaches thetemperature of the room, what is lim TE}? Use this and the information given t—lo-o to solve for all the constants 21,3, and is.