Question

A vitamin is eliminated from the blood stream at a rate of about 18% per hour. The vitamin reaches a peak level in the blood stream of 325 milligrams. Predict the amount, to the nearest tenth of a milligram, of the vitamin remaining 6 hours after the peak level.

Answer 1

Approximately 98.8 milligrams of the vitamin would remain in the bloodstream 6 hours after the peak level, calculated using the exponential decay formula with an 18% hourly decay rate.

Step-by-step explanation:

To predict the amount of a vitamin remaining in the bloodstream 6 hours after its peak level, we use the concept of exponential decay. The decay rate is 18% per hour, which means that each hour, the vitamin's concentration becomes 82% (100% - 18%) of what it was the previous hour. Starting with a peak level of 325 milligrams, we can apply the decay formula repeatedly for 6 hours.

The formula for exponential decay is: New amount = Initial amount * (1 - decay rate)^time.

In this case, we calculate the remaining amount after 6 hours using the formula: Remaining amount = 325 mg * (1 - 0.18)^6.

Calculation:
Remaining amount = 325 mg * (0.82)^6
Remaining amount = 325 mg * 0.304006
Remaining amount ≈ 98.8 mg

To the nearest tenth of a milligram, about 98.8 milligrams of the vitamin would remain in the bloodstream after 6 hours.