The half-life of Thorium 230 is about 75000 years, while that of Uranium 234 is about 245000 years.

Suppose the decay rate per atom of Uranium 234, originally assumed to be a constant kU, actually *decreases*

slowly throughout the history of the Universe, according to the rule

kU(t) = a/(1 + t/b)^2 ;

where t ranges from zero [when Uranium 234 was first created] to infinity, and where a and b are

constants [with what units?] which we can claim to know. If Uo was the initial number of Uranium 234 atoms in a given object, how many atoms of Uranium 234 will there be as t tends to infinity?

dU/dt = -kU = -a/(1 + t/b)^2

after integrate and subsitute the value of Uo, i got

U=ab^2/(b+t)+Uo-ab

when t tends to infinity, U=Uo

Is my solution correct?