Your title is wrong (many people ask questions, but the title is unclear ...)

Yes: t years later, its residual number a' is the same as the original, not ten years.

Equation: a' = AE (-kt)

Condition 1: Half-life is 5570 years. Get 1/2 = e (-k * 5570) and get the value of k 。

Condition 2: a'/a = 87.9%, 87.9% = e (-k * x). K has been determined by the condition 1 and replaced. So I got X.

This kind of problem is characterized by exponential function, the exponent or coefficient is unknown constant, and the description of the problem often involves attenuation (this kind of problem usually has no linear representation).

The solution is to ignore the decay radiation and only find the condition of undetermined coefficient, that is, the half-life condition is undetermined K.

In fact, I think it can be explained in one sentence. But you should be able to understand this kind of problem thoroughly by explaining it this way. Of course, don't miscalculate ~