1. The half-life of a radioactive substance is 140 days. An initial sample is 300 mg. a) Find the mass, to the nearest milligram, that remains after 50 days. b) After how many days will the sample decay to 200 mg? c) At what rate, to the nearest tenth of a milligram per day, is the mass decaying after 50 days?

2. The effectiveness of studying for an exam depends on how many hours a student studies. For a certain exam, a student is given one day to study. Some experiments show that if the effectiveness , is put on a scale of 0 to 6, then , where t is the number of hours spent studying for the exam. How many hours should a student study to achieve maximum effectiveness?

3. Sketch the function , indicating any x and y intercepts, extrema, and points of inflection. Show all calculations as to how such points were found.