Final answer:
The fastest drug administration method for a rapid response is intravenous (D), where the drug is directly injected into the bloodstream. For home administration of an antimicrobial for a systemic infection, the oral route (A) is most appropriate and convenient.
Step-by-step explanation:
The method of drug administration that will provide the fastest response is D) Intravenous. When a drug is administered intravenously, the drug is injected directly into the bloodstream, which allows for immediate distribution throughout the body. Consequently, the plasma levels of the drug reach their peak rapidly as there is no absorption phase needed, unlike with other administration routes such as oral or intramuscular. This is particularly important in circumstances where a rapid therapeutic effect is critical.
For the second question, the most appropriate and convenient route for home administration of an antimicrobial to treat a systemic infection would likely be A) oral. The oral route is generally preferred for home administration due to its convenience and non-invasive nature. Intravenous administration requires more specialized skills and equipment and is typically performed in healthcare settings, whereas topical application would not be effective for treating a systemic infection. Parenteral routes other than intravenous, such as intramuscular, might be appropriate in some cases but are less convenient for regular home use.