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0.5x = 0.0625

x log(0.5) = log(0.0625)

-0.30103 x = -1.20412

x = 1.20412 / 0.30103

x = 4

===========================

Check:

1/2 x 1/2 x 1/2 x 1/2 = 1/16 = 0.0625 yay!

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14y ago
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8y ago

Convert the percent to a decimal or fraction (0.125, or 1/8), and solve the equation:(1/2)^x = 1/8 (using "^" for power)

or:

0.5^x = 0.125

In this case, you can solve the problem by inspection (just try out different powers). In more difficult cases, where the solution ISN'T an integer, you can use logarithms (basically you divide the logarithm of 0.125 by the logarithm of 0.5).

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12y ago

3.125 percent of a sample is one 32nd of a sample. In the half-life scale it is the fifth half-life. (1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128, etc.)

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10y ago

four

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Q: How many half-lives should have elapsed if 12.5 percent of the parent isotope remains in a fossil at the time of analysis?
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How many half-lives have elapsed when the amount of a sample's Radioactive isotopes is reduced to 3.125 percent of the original amount in the sample?

The idea is to convert the percent to a fraction (divide it by 100), and then solve the equation: (1/2)^x = (that fraction) (Note: Using "^" for "power".) In the general case, solving this equation requires logarithms. But in this specific case, you can just try out different whole numbers for "x". # 1/2 lives vs fraction 1 0.5 2 0.25 3 0.125 4 0.0625 5 0.03175 6 0.015875 The answer falls between 5 and 6 half lives, closer to 5.

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