Answer:
16.3 hours.
Step-by-step explanation:
"Decays exponentially at a rate of 11% per hour" translates into
(1 - 0.11)^h, where h is the number of hours during which the drug decays.
The negative sign comes from "decay."
The complete formula applicable here is
d(h) = (100 mg)(1 - 0.11)^h, where h is the number of hours.
We want to know how many hours it will be until all but 15 mg remain. The appropriate formula for this is
15 mg = (100 mg)()^h. Dividing both sides by 100 mg, we get:
15 mg
------------- = 0.89^h, or 0.15 = 1.11^h
100 mg
Apply properties of logs to solve this. Take the natural log of both sides of the above equation. We get:
ln 0.15 = h(ln 0.89). Dividing both sides by ln 0.89, we get:
h = 16.3
The original 100 mg dosage would decay to 15 mg after 16.3 hours.