[labview1958 (OP)]

When a radioactive material decays, a decay curve  is drawn  for count/s vs time. Simple logic will say that the decay line should be linear with a negative slope?

[Soul Surfer]

You are thinking completely wrongly it is totally illogical that radioactive decay should be linear.  The decay of a radioactive atom is individually a probabilistic function that is, in a given time  there is a certain probability that a particular atom will decay say 50% in one year this is constant at all time so if I have a large number of these atoms half of them will decay in one year and half of those remaining will decay in the second year (ie 1/4 of the original  and half of those still remaining in the third year ie 1/8 of the original.  This is what is called an exponential decay function.

Because half decays in the first year the other half does NOT decay in the second that would result in a linear function  you are thinking that radioactive atoms each have a specific life of two years before they decay.  if that was true they would all decay on the second anniversary of when they were made!  this definitely does not happen and it is why we talk about the half life of a radioactive material and not the whole life because this is a case where two halves do NOT make a whole.

[wanhafizi]

Half lives theory said that a certain percentage of the atoms are always decaying at any given moment.

But, with the mechanism of nuclear fission where free electrons are the "triggers" and multiple free electrons are released in each reactions, it causes a chain reaction in a somewhat exponential rate, because the process keep repeating itself and involves more and more atoms...

Although the half life stays the same, we will see that the more atoms presents, the more chain reactions happened.

...I think...

[Bored chemist]

"Simple logic will say that the decay line should be linear with a negative slope?"
No it doesn't.
(ignore the timescale for the decay of uranium here, after all, I haven't said which isotope I'm using)
Imagine that it did decay linearly and I have some lump of uranium and it's decaying at 1 microgram per second.
My friend has a lump twice as big- it's logical that it would decay twice as fast- at 2 micrograms per second.
But if you wait long enough half of his lump will disapear and then he will have a lump of uranium that looks exactly the same as mine did, yet it will be decaying twice as fast.
How would a lump know how big it had been " at the start" in order to know how fast it should decay now?
(and also, how do you define "at the start"?)