# Chapter 33 - Think and Solve: 35

0.0313 milligrams. 0.000977 milligrams. Yes.

#### Work Step by Step

At 3pm, 9 hours have elapsed, which is 9/1.8 = 5 half-life periods. (1/2)(1/2)(1/2)(1/2)(1/2) = 1/32 of the original amount remains. This is 0.0313 milligram. At midnight, 18 hours have elapsed, which is 10 half-life periods. $(\frac{1}{2})^{10} =\frac{1}{1024}$ of the original, about 0.000977 milligram. Over 99.9 percent is gone by midnight. Time to make more!

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