After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after xx hours can be modeled by the function f, of, x, equals, 85, left bracket, 0, point, 9, 5, right bracket, to the power x , .f(x)=85(0.95)^x. Find and interpret the given function values and determine an appropriate domain for the function. Round your answers to the nearest hundredth.
f(−5)= blank*, meaning blank* hours after taking the dose, there are blank* milligrams of medicine remaining in the person's bloodstream. This interpretation
-makes sense
-does NOT make sense
in the context of the problem.
f(24)= blank*, meaning blank* hours after taking the dose, there are blank* milligrams of medicine remaining in the person's bloodstream. This interpretation
-makes sense
-does NOT make sense
in the context of the problem.
f(1.5)= blank*, meaning blank* hours after taking the dose, there are blank* milligrams of medicine remaining in the person's bloodstream. This interpretation
-makes sense
-does NOT make sense
in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is blank*
.
f(−5)=85(0.95)^-5 ≈ 118.05, meaning -5 hours after taking the dose, there are approximately 118.05 milligrams of medicine remaining in the person's bloodstream. This interpretation does NOT make sense in the context of the problem because time cannot be negative.
f(24)=85(0.95)^24 ≈ 28.85, meaning 24 hours after taking the dose, there are approximately 28.85 milligrams of medicine remaining in the person's bloodstream. This interpretation makes sense in the context of the problem.
f(1.5)=85(0.95)^1.5 ≈ 79.22, meaning 1.5 hours after taking the dose, there are approximately 79.22 milligrams of medicine remaining in the person's bloodstream. This interpretation makes sense in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is x ≥ 0 since time cannot be negative in this context.