Drug effectiveness decreases over time. If, each hour, a drug is only 70% as effective as the previous hour, at some point the patient will not be receiving enough
medication and must receive another dose. If the initial dose was 210 mg and the drug was administered 3 hr ago, the expression 210(0.7), which equals 72,
represents the amount
of effective medication still in the system. (The exponent is equal to the number of hours since the drug was administered.) The amount of
medication still available in the system is given by the function f(t)=210(0.7). In this model, t is in hours and f(t) is in milligrams. How long will it take for this initial dose
to reach the dangerously
low level of 50 mg?
It will take about
hours.
(Do not round until the final answer. Then round to the nearest tenth as needed.)