You go to the doctor and he gives you 11 milligrams of radioactive dye. After 20 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 Radium-226 is 1590 years. If a sample contains 100 mg, how many mg will remain after 1000 years? mg Give your answer accurate to at least 2 decimal places. The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced to a mass of 4 mg. What was the initial mass (in mg) of the sample? What is the mass (in mg) 7 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 224 grams of radioactive goo. After 120 minutes, her sample has decayed to 14 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t) =| How many grams of goo will remain after 29 minutes? You may enter the exact value or round to 2 decimal places. A wooden artifact from an ancient tomb contains 25 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.) years A bacteria culture initially contains 1500 bacteria and doubles every half hour. Find the size of the baterial population after 40 minutes. Find the size of the baterial population after 4 hours. The doubling period of a bacterial population is 10 minutes. At time t = population was 50000. What was the initial population at time t = 0? Find the size of the bacterial population after 5 hours. 120 minutes, the bacterial The count in a bacteria culture was 900 after 20 minutes and 1700 after 40 minutes. Assuming the count grows exponentially, What was the initial size of the culture? Find the doubling period. Find the population after 120 minutes. When will the population reach 11000. You may enter the exact value or round to 2 decimal places. Find the time required for an investment of 5000 dollars to grow to 7900 dollars at an interest rate of 7.5 percent per year, compounded quarterly. Your answer is t = years. You may enter the exact value or round to 2 decimal places. The fox population in a certain region has a continuous growth rate of 7 percent per year. It is estimated that the population in the year 2000 was 13800. (a) Find a function that models the population t years after 2000 (t = 0 for 2000). Hint: Use an exponential function with base e. Your answer is P(t)= | (b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer must be an integer)