Problem 3

Problem 3. Let f(x) = 12. In this problem you will check that f is a convex (a.k.a. concave up) function. Show that for all a 12. Problem 4. A sample of an unknown radioactive isotope was delivered to a laboratory. On the day the sample was delivered its mass was 2021 grams, and 28 days later the mass of the sample was 2019 grams. It is known that the mass of radioactive isotopes decays according to an exponential function. 1. What is the half-life of the unknown radioactive isotope? Give your answer to the nearest day. 2. It took 14 days for the sample to be delivered. What was the mass of the sample at the time it was shipped? Give your answer to the nearest gram. Problem 5. Let f : (-co, 0] -> R be the function defined by f(x) = . Is f invertible? If the answer is yes, determine the domain and range of f-1, and determine a formula for f-1(x)