Math Problem Statement

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, 120, left parenthesis, 0, point, 8, 6, right parenthesis, to the power x , .f(x)=120(0.86) 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, of, minus, 3, 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, of, 42, equalsf(42)= , 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, of, 8, point, 5, equalsf(8.5)= , 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

Solution

It seems like I can’t do more advanced data analysis right now. Please try again later. Let me know if you have any other questions or if you'd like me to assist with anything else.

In the meantime, here are a few questions related to the problem for you to consider:

  1. What does the parameter 0.86 in the function represent in terms of the decay rate of the medication?
  2. How would you interpret the function for values larger than 42 hours?
  3. Is the medication completely gone from the bloodstream at some point, or does it approach zero asymptotically?
  4. How would the interpretation change if the base of the exponent were greater than 1?
  5. What would the initial amount of medicine in the bloodstream be at time t = 0?

Tip: When analyzing functions with exponential decay, the base of the exponent gives insights into how quickly the quantity decreases over time.

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Math Problem Analysis

Mathematical Concepts

Exponential Decay
Functions
Algebra

Formulas

f(x) = 120(0.86)^x

Theorems

Exponential decay behavior
Asymptotic behavior

Suitable Grade Level

Grades 9-12