To analyze the equation \( y = 500(0.85)^x \), which represents the amount of drug remaining in a patient's system after \( x \) hours, we note that this is an exponential decay function.
As \( x \) increases (meaning more time passes), the term \( (0.85)^x \) becomes very small because the base, 0.85, is less than 1. This means that the amount \( y \) will decrease over time.
As \( x \) approaches infinity (as time goes on indefinitely), \( (0.85)^x \) approaches 0, and consequently, \( y \) approaches 0.
Now, let's evaluate the response options:
A. The number of milligrams in the body will approach 0. (Correct)
B. The number of milligrams in the body will be 100 or more. (Incorrect)
C. The number of milligrams will reach a maximum of 600. (Incorrect)
D. The number of milligrams will approach 100. (Incorrect)
The correct response is A: The number of milligrams in the body will approach 0.
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