If half of a radioactive sample decays after 1 day, will the other half decay after 1 additional day? Why or why not?
No - half of the other half will decay in the next day.
Now, at the start of the next day, those isotopes that are radioactive.....if you look only at the ones that are radioactive, then 100% of the radioactive isotopes are still radioactive. And in this next day, 100% of those radioactive isotopes will decay into 50% radioactive, 50% non radioactive.
On the next day, of the sample that is radioactive, 100% are radioactive.....and they will decay into 50% radioactive, 50% non radioactive....and so on and so on.
But each day, the total population of radioactive isotopes is decreasing by (1/2). 50% first day, 25% next day, 12.5% following day, 6.25%..and so on.