When does a radioactive sample emit the largest number of decay particles? why is this information important? (how can it be applied in our world today? )

A radioactive sample emits the most radiation as soon as it is formed or isolated. The reason is that that is when the concentration of the radioactive material is the greatest. It begins to decay immediately and as it does, the concentration of radioactive material in the sample gets less. This process can take milliseconds or millions of years depending upon the rate at which the substance breaks down. The reason it's important is that we need to know how long a radioactive material will take to decay to the point that there is so little left that it no longer poses a threat to life.