A radioactive isotope decays at the rate indicated by the exponential function LaTeX: A\left(t\right)=400\left(\frac{1}{2 }\right)^{\frac{t}{100}}A ( t ) = 400 ( 1 2 ) t 100, where 't' is the time in year and A(t) is the amount of the isotope, in grams, remaining. How long will it take for the isotope to be reduced to half of its original amount?