A vitamin degrades in the body according to the function represented in the table, where [tex]$x$[/tex] is the time in hours and [tex]$f(x)$[/tex] is the dosage in milligrams. What was the original dose?
A. 0.50 milligrams
B. 8 milligrams
C. 24 milligrams
D. 500 milligrams
Answer (2)
The problem asks for the original dose of a vitamin, which is the dosage at time x = 0 .
The table provides the dosage f ( x ) at different times x .
From the table, when x = 0 , f ( x ) = 500.00 milligrams.
Therefore, the original dose of the vitamin was 500 milligrams.
Explanation
Understanding the Problem The problem provides a table showing the dosage of a vitamin in milligrams at different times in hours. We need to find the original dose of the vitamin, which is the dosage at time x = 0 .
Finding the Original Dose The table gives the dosage f ( x ) at different times x . We look for the value of f ( x ) when x = 0 . From the table, we see that when x = 0 , f ( x ) = 500.00 milligrams.
Final Answer Therefore, the original dose of the vitamin was 500 milligrams.
Examples
Understanding how substances degrade over time is crucial in many real-world applications. For example, in medicine, knowing the degradation rate of a drug helps doctors determine the correct dosage and frequency to maintain therapeutic levels in the body. Similarly, in environmental science, understanding how pollutants degrade helps scientists assess the long-term impact on ecosystems. In food science, it helps determine the shelf life of products and ensure food safety. This concept is also used in forensic science to estimate the time of death based on the decomposition rate of a body.
The original dose of the vitamin is determined by finding the dosage at time x = 0 , which is 500 milligrams. Therefore, the correct answer is 500 milligrams. This dosage is key for understanding how the vitamin degrades within the body over time.
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