Answer:The appropriate domain for this function is x ≥ 0, meaning x can take on any non-negative real value.
The given function is:
F(x) = 110 (0.83)^x
Here, x represents the number of hours that have passed since taking the medication, and F(x) represents the amount of medicine remaining in the person's bloodstream after x hours.
Let's calculate some function values to interpret their meaning:
F(0) = 110 (0.83)^0 \n\n =110 * 1 \n\n= 110
When x = 0 (right after taking the medication), there are 110 milligrams of medicine in the bloodstream.
This is the initial dosage.
F(1) = 110 (0.83)^1 \n\n\approx 91.3
After 1 hour, approximately 91.3 milligrams of the medicine remain in the bloodstream.
F(2) = 110 (0.83)^2 \n\n\approx 75.9
After 2 hours, approximately 75.9 milligrams of the medicine remain in the bloodstream.
Interpretation:
As time passes (represented by increasing values of x), the amount of medicine in the bloodstream decreases. This decrease is exponential, as indicated by the exponentiation with 0.83. The medicine is being metabolized or eliminated from the body over time.
Domain of the function:
Since time cannot be negative (you can't take the medication before you've taken it), the domain of the function should be limited to non-negative values of x. So, the appropriate domain for this function is x ≥ 0, meaning x can take on any non-negative real value. This ensures that we are only considering valid time intervals after taking the medication.
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Step-by-step explanation:
