Acertain radioactive isotope placed near a geiger counter registers 120 counts per minute. if the half-life of the isotope is one day, what will the count rate be at the end of four days?

The count rate at the end of four days will be 7.5 counts per minute.

Explanation:

First it is important to know that half-life is the time to a piece of radioactive material to decay 50%. So if we know we start with 120 counts per minute and we already know the half-life of the isotope is 1 hour we expect that past 1 hour the material decays 50% (it's halved) so we will count 60 counts per minute, now if we wait another hour 60 counts will decay in to 30 counts per minute and so on. That should be translate to a math equation as:

final counts = initial counts *

After 4 days we have 4 half-life periods passed so:

final counts= 120 counts per minute *

final material = 7.5 counts per minute