Question

A substance with a half life is decaying exponentially. If there are initially 12 grams of the substance and after 2 hours there

are 7 grams, how many grams will remain after 3 hours? Round your answer to the nearest hundredth, and do not include
units.
Provide your answer below:

Answer 1

5.35 grams

Explanation:

Given that a 12 grams of a substance will decay exponentially to 7 grams in 2 hours, you want to know the amount remaining after 3 hours.

Equation

The amount remaining can be described by ...

remaining = (initial amount)·(decay factor)^(t/(decay interval))

remaining = 12(7/12)^(t/2) . . . . where t is in hours

Application

After 3 hours, the amount remaining is ...

remaining = 12(7/12)^(3/2) ≈ 5.35 . . . . grams

About 5.35 grams will remain after 3 hours.

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Additional comment

The half-life is about 2.572 hours.