How do i use exponential decay models with radioactive isotopes and their life spans?

Specifying the half life or mean life of a process is a way of quantifying how fast it is occurring, when the whole process would in principle take forever to complete.  The example we will talk about here is radioactive growth and decay, but examples from other fields include the recovery of a muscle after some exertion, and the filling of a cistern.

In particular then, the half life of a radioactive element is the time required for half of it to decay (i.e. change into another element, called the "daughter" element).

So if a radioactive element has a half life of one hour, this means that half of it will decay in one hour.  After another hour, half of the remaining material will decay.  But why didn't all of that remaining material decay in that second hour?  Does the element somehow know that it's decaying, and alter its decay speed to suit?

Textbooks are usually content with deriving of the law of decay, and don't tend to address this question.  And yet it forms a classic example of the way in which research in physics (and science in general) is carried out.  Regardless of how we might expect an element to behave—where perhaps the second half might be expected to decay in the same amount of time as the first half—this simply does not happen.  We must search for a theory that predicts this.

Science is often thought to proceed by our logically deducing the laws that govern the world.  But it's not that simple; there are limits to what we can deduce, especially about things in which we cannot directly participate.  Radioactive decay is a good example of this.  We can't use a microscope to watch the events that make an element decay.  The process is quite mysterious.  But what we can do is make a simple theory of how decay might work, and then use that theory to make a prediction of what measurements we can expect.  That's the way science proceeds: by making theories that lead to predictions.  Sometimes these predictions turn out to be wrong.  That's fine: it means we must tinker with the theory, perhaps discard it outright, or maybe realise that it's completely okay under certain limited circumstances.  The hallmark of a good scientific theory is not what it seems to explain, but rather what it predicts.  After all, a theory that says the universe just appeared yesterday, complete with life on earth, fossils and so on, in a sense "explains" everything beautifully by simply defining it to be so; but it predicts absolutely nothing.  So from a scientific point of view it is not a very useful theory, because it contains nothing that allows its truth to be tested.  On the other hand, while it's arguable that the theory of quantum mechanics explains anything at all, it certainly does predict a huge number of different phenomena that have been observed; and that's what makes it a very useful theory.

6in^2

Step-by-step explanation:

formula of a triangle: l x h : 2

4 x 3 = 12

12 : 2 = 6^2