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1. Bacteria grow in a nutrient solution at a rate the well-stirred mixture leaves the tank at the same proportional to the amount present. Initially. there rate. Find the amount of salt in the tank at any time 1. are 250 strands of the bacteria in the solution which a. Q m -Se"" +5 c. Q - -2.5e-1+ 5 grows to 800 strands after seven hours. Find an b. Q - -Se-021 +5 d. Q - -25e-02 +5 expression for the approximate number of strands in the culture at any time t. 6. A body of mass 2 kg is dropped from a height of AN = 250e01661 C. N = 1250.16 6t 200 m. Find the limiting velocity of the body if it b. N = 250e01 164 d. N = 12501 16t encounters a resistance force equal to -50v. a. 1.794 m's c. 0.897 m/'s 2. A certain radioactive material is known to decay b. 0.348 m/'s d. 0.392 m/s at a rate proportional to the amount present. If initially there are 100 milligrams of the material 7. The population of a certain state is known to grow present and if after two years, it is observed that S at a rate proportional to the number of people percent of the original mass has decayed, find the presently living in the state. If after 10 years the time necessary for 10 percent of the original mass to population has trebled and if after 20 years the have decayed. population is 150,000, find the number of people a. 3.16 yrs c. 2.26 yrs initially living in the state. b. 4.05 yrs d. 1.84 yrs a. 15120 c. 24610 516620 d. 8820 3. A body of unknown temperature is placed in a refrigerator at a constant temperature of 0% F If after 8. A tank contains 100 gal of brine made by 20 minutes the temperature of the body is 40 F and dissolving 80 lb of salt in water. Pure water runs into after 40 minutes the temperature of the body is 20 the tank at the rate of 4 gal/min, and the well-stirred F. find the initial temperature of the body. mixture runs out at the same rate. Find the time a. 40 F C. 80OF required for half the salt to leave the tank. b. 30.F d. 60OF a. 17.3 min c. 8.13 min b. 24.6 min d. 10.9 min 4. A hot pie that was cooked at a constant temperature of 325 F is taken directly from an oven 9. A certain radioactive material is known to decay and placed outdoors in the shade to cool on a day at a rate proportional to the amount present. If after when the air temperature in the shade is 85 F. After one hour it is observed that 10 percent of the material 5 minutes in the shade, the temperature of the pic had has decayed. find the half-life of the material. been reduced to 250 F. Determine the temperature a. 6.6 hrs c. 4.7 hrs of the pie after 20 min. b. 3.2 hrs d. 8.2 hrs a. 125.1 F C. 138.6.F b. 88.83.F d. 178.2 F 10. Find the general solution of the differential equation x?y' + 2xy = 5. 5. A tank initially holds 10 gal of fresh water. All = a. 2x y - 3x = C c. xly - 5x = C 0. a brine solution containing y lb of salt per gallon b. 2xy? + x = C d. #xy2 + 5x = C is poured into the tank at a rate of 2 gal/min, while