1. Scientist can determine the age of ancient objects by a method called raarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radfoactive isotope of carbon, 14C, with a half-life of about 5730 years. VegetatIon absorbs carbon dIcalde through the atmosphere and animal life assImflates 14C through food chains. When a plant or 371.1 dies, It stops replacIng its carbon and the amount of 14C beg. to /decrease through radioactive decay. Therefore, the level of radioactivity must also decay exponentially.
A parchment fragment was discovered Mat 734 about 64% as much 14C radioactivity 66 0066 plant material on Earth today. Estimate the age of the parchment. (Pound your answer to the nearest hundred years.)
2. x In x =y(1 + √(24 + y2)) y', y(1) = 1.
3. Find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) Is 5xy.
4. A tank contains 300 L of 15rne with 16 kg of dissolved salt. Pure water enters the tank at a rate of 30 L/min. The solution is kept thoroughly mIxed and drains from the tank at the same rate.
(a) How much salt is In the tank after t minutes,
(b) How much salt is In the tank after 30 minutes, (Round your answer to one decIrnal place.) y =
5. A roast turkey Is taken from an oven when Its Mmperature has reached 185°F and is placed on a table In a room where the temperature 75°F. (Round your answers to the nearest whole numher.)
(a) If the temperature of the turkey Is 150°F after half an hour, what Is the temperature after 50 minutes,
(b) When the turkey have cooled to 95°7
6. A sample of a radioactive substance decayed to 96% of original amount after a year. (Round your answers to two decimal Places.)
(a) What is the half-life of the substance,
(b) How long would It take the sample to decay to 90% 00 109 orIginal amount,