Paracelsus is famous for saying that “all substances are poisons; there is none which is not a poison. The right dose differentiates a poison from a remedy.” Explain what he meant by this statement. Illustrate your point using a graded dose-response curve

A 31-year-old patient develops a severe full-body rash almost immediately after receiving penicillin. Describe what is likely the cause of the rash. [Hint - this is asking about hypersensitivity]

Bryan is a physician at a major metropolitan hospital. Since the attacks of September 11, 2001, his hospital has been preparing for a terrorist attack. Why does the CDC recommend using antibiotics only when exposure to disease is suspected or confirmed?

First, we will build a model for the total amount of drugs in the gut. At time \(t = 0\), \(10mg\) of the drug is present in the gut. From the gut, it passes slowly into the blood. The passage of the drug to the blood has first-order kinetics; that is, every hour \(42\%\) of the drug remaining in the gut is passed from the gut into the blood. No more pills are taken, so no extra drug is added to the gut.   Let \(a_t\) be the sequence representing the amount of Adderall XR in the patient’s gut \(t\) hours after the pill was taken. Write down a recursion relation for \(a_t\).   Find an explicit formula for \(a_t\).   Calculate the time at which the amount of drug remaining in the gut drops to \(1\%\) of its starting value; that is, find \(t\) for which \[a_t = 0.01a_0\] Find \(\lim_{t\to\infty}a_t\), what does it represent?   Now let’s build a model for the amount of drug in the patient’s blood. Define another sequence \(b_t\) that represents the amount of Adderall XR in the patient’s…