(20 points) A typical cup of coffee contains about 100 mg of caffeine. After drinking a cup of coffee, the caffeine is absorbed into the bloodstream, metabolized, and then eliminated. Assume the amount of caffeine in the body decays exponentially and that 3 hours after drinking a cup of coffee, approximately 65 mg of caffeine remains in the body. a) What is the hourly decay factor? b) What is the hourly decay rate? (Write the exact value) c) Write a function for the amount C of caffeine in the body in mg as a function of the number of hours, t. since drinking a cup of coffee. d) Use the function to determine when the level of caffeine in the body falls to 30 mg (Write the exact value)