Answer:
The appropriate domain for the function is [0, ∞).
Explanation:
Given function: f(x) = 120 (0.86)x
To find the function values, we can substitute the given value of x into the function:
f(0) = 120 (0.86)^0 = 120 (1) = 120
Interpretation: When the medication is first taken, there are 120 milligrams of medicine in the person's bloodstream.
f(2) = 120 (0.86)^2 ≈ 84.24
Interpretation: After 2 hours, there are approximately 84.24 milligrams of medicine remaining in the person's bloodstream.
f(6) = 120 (0.86)^6 ≈ 34.17
Interpretation: After 6 hours, there are approximately 34.17 milligrams of medicine remaining in the person's bloodstream.
The domain of the function is all non-negative real numbers, since the amount of medicine in the bloodstream can't be negative and time is measured in non-negative hours. So the appropriate domain for the function is [0, ∞).