I don't think this is an exponential decay.

First, x is incremented by same amount, 10 years, each step. However, y is not reduced by the same factor.

25165824 / 393216 = 64 but

393216 / 12288 = 32

showing that y is not exponential.

Also, if it was some kind of multiplicative reduction, y would never reach 0.

Is there any more information for the problem?