The function m, defined by m(h) = 300 · (_3
4)
h
, represents the amount of a
medicine, in milligrams, in a patient’s body. h represents the number of
hours after the medicine is administered.
a. What does m(0.5) represent in this situation?
Lesson 4-3 Understanding Rational Inputs 21
b. This graph represents the function m.
Use the graph to estimate m(0.5).
c. Suppose the medicine is administered
at noon. Use the graph to estimate the
amount of medicine in the body at
4:30 p.m. on the same day.
Answers
Answer:
B is the correct oneSuppose the medicine is administered
at noon.
Answer:
a. To find m(0.5), we substitute 0.5 for h in the function m(h):
m(0.5) = 300 · (_3/4)^0.5 = 300 · (√3/2) ≈ 259.81
Therefore, m(0.5) represents the amount of medicine, in milligrams, in the patient's body 0.5 hours after the medicine is administered.
b. Looking at the graph, we can estimate m(0.5) by finding the point on the y-axis where x = 0.5. We can see that the graph intersects the y-axis at approximately 260, which is very close to the exact value we calculated in part a.
c. To estimate the amount of medicine in the body at 4:30 p.m., we need to find the value of m when h = 4.5. Looking at the graph, we can see that at 4 hours, the amount of medicine is approximately 225 milligrams. From there, we can estimate that at 4.5 hours, the amount of medicine will be slightly higher, at approximately 235 milligrams.
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