Question

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, left bracket, x, right bracket, equals, 60, left bracket, 0, point, 8, 5, right bracket, to the power x , .f(x)=60(0.85) x . find and interpret the given function values and determine an appropriate domain for the function. round your answers to the nearest hundredth. answer attempt 1 out of 2 f, left bracket, minus, 3, right bracket, equalsf(−3)= , meaning hours after taking the dose, there are milligrams of medicine remaining in the person's bloodstream. this interpretation in the context of the problem. f, left bracket, 24, right bracket, equalsf(24)= , meaning hours after taking the dose, there are milligrams of medicine remaining in the person's bloodstream. this interpretation in the context of the problem. f, left bracket, 6, point, 5, right bracket, equalsf(6.5)= , meaning hours after taking the dose, there are milligrams of medicine remaining in the person's bloodstream. this interpretation in the context of the problem. based on the observations above, it is clear that an appropriate domain for the function is .

a. f(−3)=___, meaning hours after taking the dose, there are milligrams of medicine remaining in the person's bloodstream. This interpretation in the context of the problem.

b. f(24)=___, meaning hours after taking the dose, there are milligrams of medicine remaining in the person's bloodstream. This interpretation interpretation in the context of the problem.

c. f(6.5)=___, meaning hours after taking the dose, there are milligrams of medicine remaining in the person's bloodstream. This interpretation in the context of the problem.

d. None of the above

Answer 1

To find the values of f(-3), f(24), and f(6.5), substitute the values of x into the function 60(0.85)^x and evaluate. The interpretation of these values in the context of the problem is provided. The appropriate domain for the function is the set of all real numbers.

Step-by-step explanation:

To find the values of f(-3), f(24), and f(6.5) using the function f(x) = 60(0.85)^x, we simply substitute the given values of x into the function and evaluate:

f(-3) = 60(0.85)^(-3) ≈ 87.65

f(24) = 60(0.85)^24 ≈ 0.31

f(6.5) = 60(0.85)^6.5 ≈ 5.09

In the context of the problem, f(-3) represents the amount of medicine remaining in the person's bloodstream after 3 hours, f(24) represents the amount of medicine remaining after 24 hours, and f(6.5) represents the amount of medicine remaining after 6.5 hours.

Based on the observed values, an appropriate domain for the function is the set of all real numbers (-∞, ∞).