Question
A medication loses 3%
per hour. The initial dose is 200
mg.
Which expression shows the amount left after 12
hours?
Click Here for a Hint
(2 points)
Responses
200(0.97)^12
200 times 0 point 9 7 to the 12th power
200(0.97)(12)
200 0 point 9 7 12
200(0.03)^12
200 times 0 point 0 3 to the 12th power
200(1.03)^12
per hour. The initial dose is 200
mg.
Which expression shows the amount left after 12
hours?
Click Here for a Hint
(2 points)
Responses
200(0.97)^12
200 times 0 point 9 7 to the 12th power
200(0.97)(12)
200 0 point 9 7 12
200(0.03)^12
200 times 0 point 0 3 to the 12th power
200(1.03)^12
Answers
GPT-4o mini
To find the amount of medication left after 12 hours, you can use the formula for exponential decay. Since the medication loses 3% per hour, 97% of the medication remains after each hour, which is represented by 0.97.
The amount left after \( t \) hours can be expressed as:
\[
\text{Amount Left} = \text{Initial Amount} \times (0.97)^t
\]
In this case, the initial dose is 200 mg, and \( t \) is 12 hours. Therefore, the expression to show the amount left after 12 hours is:
\[
200(0.97)^{12}
\]
Thus, the correct response is:
**200(0.97)^{12}**
The amount left after \( t \) hours can be expressed as:
\[
\text{Amount Left} = \text{Initial Amount} \times (0.97)^t
\]
In this case, the initial dose is 200 mg, and \( t \) is 12 hours. Therefore, the expression to show the amount left after 12 hours is:
\[
200(0.97)^{12}
\]
Thus, the correct response is:
**200(0.97)^{12}**