Question

The graph of y = 500(0.85)x represents the number of milligrams of a drug, y, are left in a patient’s system x hours after it was administered.


Amount of Drug Left
Number of Milligrams

Number of Hours

What eventually happens to the amount of drug left in the patient’s system?
Responses
A The number of milligrams in the body will approach 0.The number of milligrams in the body will approach 0.
B The number of milligrams in the body will be 100 or more.The number of milligrams in the body will be 100 or more.
C The number of milligrams will reach a maximum of 600.The number of milligrams will reach a maximum of 600.
D The number of milligrams will approach 100.

Answer 1

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.**