How do you Find exponential decay rate?
1 Answer
See below.
Explanation:
Exponential decays typically start with a differential equation of the form:
That is, the rate at which a population of something decays is directly proportional to the negative of the current population at time
We will now solve the equation to find a function of
This is the general form of the exponential decay formula and will typically have graphs that look like this:
graph{e^-x [-1.465, 3.9, -0.902, 1.782]}
Perhaps an example might help?
Consider a lump of plutonium 239 which initially has
We are told the lump has
Now at 1 million years:
Rearrange to get:
So
For the next part:
Rearrange to get
Now for the last part, the decay rate is already defined a way back at the very start, simply evaluate it at the given time:
The idea is to start with differential equation above, which gives the decay rate, and solve it to get the population at any given time.