Question
After a certain medicine is injected, its concentration in the bloodstream changes exponentially over time.
The graph describes the medicine's concentration (in milligrams per liter) over time (in hours).
A graph with time, in hours, on the horizontal axis and concentration, in milligrams per liter, on the vertical axis. A decreasing exponential function passes through the point (0, 100) and the point (1,70).
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{7}\]
\[\small{10}\]
\[\small{20}\]
\[\small{30}\]
\[\small{40}\]
\[\small{50}\]
\[\small{60}\]
\[\small{70}\]
\[\small{80}\]
\[\small{90}\]
\[\small{100}\]
What does the graph suggest about the medicine's concentration beyond
\[8\] hours?
Choose 1 answer:
Choose 1 answer:
(Choice A) The medicine's concentration will become
\[0\].
A
The medicine's concentration will become
\[0\].
(Choice B) The medicine's concentration will become negative.
B
The medicine's concentration will become negative.
(Choice C) The medicine's concentration will begin to increase.
C
The medicine's concentration will begin to increase.
(Choice D) The medicine's concentration will continue to approach
\[0\] while remaining positive.
D
The medicine's concentration will continue to approach
\[0\] while remaining positive.
The graph describes the medicine's concentration (in milligrams per liter) over time (in hours).
A graph with time, in hours, on the horizontal axis and concentration, in milligrams per liter, on the vertical axis. A decreasing exponential function passes through the point (0, 100) and the point (1,70).
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{7}\]
\[\small{10}\]
\[\small{20}\]
\[\small{30}\]
\[\small{40}\]
\[\small{50}\]
\[\small{60}\]
\[\small{70}\]
\[\small{80}\]
\[\small{90}\]
\[\small{100}\]
What does the graph suggest about the medicine's concentration beyond
\[8\] hours?
Choose 1 answer:
Choose 1 answer:
(Choice A) The medicine's concentration will become
\[0\].
A
The medicine's concentration will become
\[0\].
(Choice B) The medicine's concentration will become negative.
B
The medicine's concentration will become negative.
(Choice C) The medicine's concentration will begin to increase.
C
The medicine's concentration will begin to increase.
(Choice D) The medicine's concentration will continue to approach
\[0\] while remaining positive.
D
The medicine's concentration will continue to approach
\[0\] while remaining positive.
Answers
Answered by
GPT-4o mini
Based on the information provided about the exponential decay of the medicine's concentration, we can analyze the situation:
1. The concentration of the medicine starts at 100 milligrams per liter at time \( t = 0 \) hours and decreases over time.
2. At \( t = 1 \) hour, the concentration decreases to 70 milligrams per liter. This reflects a decreasing exponential function, which means that the concentration will continue to decrease as time progresses.
In the context of exponential decay, while the concentration of the medicine will get very small over time, it will never actually reach zero or become negative. The graph suggests that it will asymptotically approach 0, meaning it will get closer and closer to 0 but will always remain positive.
Given these considerations, the most accurate conclusion is:
**(Choice D)** The medicine's concentration will continue to approach \( 0 \) while remaining positive.
1. The concentration of the medicine starts at 100 milligrams per liter at time \( t = 0 \) hours and decreases over time.
2. At \( t = 1 \) hour, the concentration decreases to 70 milligrams per liter. This reflects a decreasing exponential function, which means that the concentration will continue to decrease as time progresses.
In the context of exponential decay, while the concentration of the medicine will get very small over time, it will never actually reach zero or become negative. The graph suggests that it will asymptotically approach 0, meaning it will get closer and closer to 0 but will always remain positive.
Given these considerations, the most accurate conclusion is:
**(Choice D)** The medicine's concentration will continue to approach \( 0 \) while remaining positive.