According to Johns Hopkins Medical Center, the half-life of caffeine in the body of adults is between 4 and 6 hours. For this lab assignment, we will assume the half-life is 5 hours. 1. Find an exponential function of the form f(t) = C-bt, that gives the amount, f(t), of caffeine present in the body t hours after a person consumes 150 mg of caffeine. Hint: How much caffeine is present at t = 0 hours? How much caffeine is present after t = 5 hours? 2. Sketch the graph of y = f(t). 3. How long will it take for the amount of caffeine present in the body to reach 50 mg? Hint: How do you rewrite an equation of the form y = bx so that it does not involve exponentials? 4. Find a function, g(x), that gives the amount of time required for the amount of caffeine present in the body to drop to x mg. 5. Sketch the graph of the function y = g(x).