The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours it is observed that 600 bacteria are present. After 10 hours 2000 bacteria are present. What was the initial population of bacteria?
Initially 100 milligrams of a radioactive substance was present. After 5 hours the mass had decreased by 6%. If the rate of decay is proportional to the amount of substance present at time t, determine the half life of the radioactive substance. (Round your answer to one decimal place)
A thermometer is removed from a room where the temperature is 21 deg C and is taken outside. Where the air temperature is -10 deg C. After one-half minute the temperature reads 12 deg C. What is the reading of the thermometer at t = 1 min? (round your answer to two decimal places) How long will it take for the thermometer to reach -8 deg C? round your answer to two decimal places)
A dead body was found within a closed room of a house where the temperature was a constant 21 deg C. At the time of discovery the core temperature of the body was determined to be 28 deg C. One hour later a second measurement showed that the core temperature of the body was 25 deg C. Assume that the time of death corresponds to t = 0 and that the core temperature at that time was 37 deg C. Determine how many hours elapsed before the body was found. [Hint: Let t1 > 0 denote the time that the body was discovered](Round your answer to one decimal place)
A tank contains 360 liters of fluid in which 40 grams of salt are dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6L/min ; the well mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.