Asample originally contained 1.28 g of a radioisotope. it now contains 1.12 g of its daughter isotope.

how many half-lives have passed since the sample originally formed?

3
4
8
16

The answer is 3.

The relation between number of half-lives (n) and decimal amount remaining (x) can be expressed as:



We need to calculate n, but we need x to do that. To calculate what percentage of a radioactive species would be found as daughter material, we must calculate what amount remained:
1.28 - 1.12 = 0.16

If 1.28 is 100%, how much percent is 0.16:
1.28 : 100% = 0.16 : x
x = 12.5% 
Presented as decimal amount:
x = 0.125

Now, let's implement this in the equation: 



Because of the exponent, we will log both sides of the equation:






Therefore, 3 half-lives have passed  since the sample originally formed.

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