Malcolm is diagnosed with an ear infection, and the doctor prescribes him an antibiotic. His initial dose is 450 mg, but after that, he is given 200 mg every 8 hours. Assume that his body eliminates 70% of the drug from his system every 8 hours. 1. Write a set of recursive equations that models the amount of antibiotic, , in his system, including your definition of. 2. Malcolm takes his first dose at 11 pm on Thursday. What amount of antibiotic is in his system at 3 pm on Friday? Show how you arrived at your answer. 3. If Malcolm follows these instructions, what is the amount of antibiotic in his system in the long run? (To receive full credit, you must solve for this value algebraically.)