Acertain isotope decays so that the amount a remaining after t years is given by: a = a0 · e ^-0.03t where a0 is the original amount of the isotope. to the nearest year, the half-life of the isotope (the amount of time it takes to decay to half the original amount) is how many years?

Ending Amt = Bgng Amt * e ^-0.03t
In this equation, the "-0.03" is the decay factor or "k"
We can now solve for half-life by this equation:
t = (ln [y(t) ÷ a]) ÷ -k  (we can say beginning amount = 200 and ending amount = 100
t = (ln [200 ÷ 100]) ÷ -k
t = (ln [2]) ÷ -k
t = 0.69314718056 ÷ --.03
t = 23.1049060187
about 23 years