Question

The milligrams of aspirin in a person’s body is given by the function a(t)= 500(3/4)^t, where t is the number of hours since the patient took the medicine. How many milligrams of aspirin will be in the patient’s body after 2 hours

Answer 1

To determine how many milligrams of aspirin remain in the patient's body after 2 hours, substitute t=2 into the function a(t) = 500(3/4)^t. The calculation yields 281.25 milligrams of aspirin after 2 hours.

Step-by-step explanation:

The student's question involves the calculation of the remaining milligrams of aspirin in a person's body after a certain amount of time, using an exponential decay function.

This is a typical high school level mathematics problem involving the application of functions to real-world situations.

To find how many milligrams of aspirin will be in the patient’s body after 2 hours, we need to substitute the value of t=2 into the given function a(t) = 500(3/4)^t.

Therefore, the calculation would be a(2) = 500(3/4)^2.

First, calculate (3/4)^2:

• (3/4)^2 = 3/4 * 3/4 = 9/16

Next, multiply this result by 500:

• 500 * 9/16 = 281.25

So, 281.25 milligrams of aspirin will be in the patient’s body after 2 hours.