請問這題微積分怎麼解?

The general formula for radioactive decay is given by
Q(t)=A(2^(-t/T)
where
t=elapsed time
A=quantity (mass) at t=0
T=half-life, and
Q(t) = remaining amount at time t.

For T=1690 years, A=50 g, we have
and Q(t)=5 g
We set up the eqation
5=Q(t)=50(2^(-t/1690)
=>
2^(-t/1690)=5/50=1/10
take log to base 2
-t/1690=log(1/10)/log(2)
t=-1690log(0.1)/log(2)=5614.06 years
Check:
Q(5614.06)=50(2^(-5614.06/1690)=5.00000...ok