please help

You go to the doctor and he gives you 13 milligrams of radioactive dye. After 12 minutes, 5 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute. You will spend minutes at the doctor's office. The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced to a mass of 7 mg. What was the initial mass (in mg) of the sample? What is the mass (in mg) 4 weeks after the start? You may enter the exact value or round to 4 decimal places. At the beginning of an experiment, a scientist has 248 grams of radioactive goo. After 150 minutes, her sample has decayed to 15.5 grams. What is the half-life of the goo in minutes? Z] Find a formula for G(t), the amount of goo remaining at time t. 00*) = How many grams of goo will remain after 71 minutes? C] _You may enter the exact value or round to 2 decimal places. A wooden artifact from an ancient tomb contains 40 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) A bacteria culture initially contains 2000 bacteria and doubles every half hour. Find the size of the baterial population after 40 minutes. :] Find the size of the baterial population after 10 hours. :] The doubling period of a bacterial population is 10 minutes. At time t = 100 minutes, the bacterial population was 80000. What was the initial population at time t = 0? Find the size of the bacterial population after 5 hours. The count in a bacteria culture was 400 after 10 minutes and 1600 after 35 minutes. Assuming the count grows exponentially, What was the initial size of the culture? :] Find the doubling period. Z] Find the population after 100 minutes. C] When will the population reach 13000. You may enter the exact value or round to 2 decimal places