Exponential decay and inverse realtionships??

Question

What is the difference between an exponential decay model and an inverse relationship between two variables? And could you give a real life situation for these and explain the differences between them too?

Use whatever you need (graphs, eqations, tables, whatever) to explain them. thanks for the help. i really don't understand all of this.

thank you for trying to help me!!

Answer 1

The difference between exponential decay and inverse relationships between two variables is as follows. Exponential decay refers primarily to rates of radioactive decay. You have a rate of decay over time for some element, say 1/e^(.2x) to keep it simple, and you compare it with the amount of the the element over that same time period. It's called exponential when its rate decreases at a rate proportional to its value. An inverse relationship is easier to describe and conceive. An inverse relationship is one where one variable increases while the other one decreases, in a simple one-to-one manner.

Answer 2

Inverse Exponential

Answer 3

An exponential decay model would be of the form
y = k*e^(-cx) where k and c are constants
while two variables that are inversely proportional to each other must obey the equation y = c/x. In both instances, increasing x will cause y to decrease and vice versa. This is really where the similarities end.

Typically exponential decay models are used to examine radioactive decay. x in this case should really be t for time, while y is the remaining mass of a certain substance, k is the initial mass of the substance, and c is a rate constant that specifies how quickly the substance is decaying. Radioactive substances follow this model because their rate of decay is proportional to the amount of substance remaining (if there's a lot of it, it decays pretty fast, if there's not so much of it, it decays slowly). Take a look at the graph of a decaying exponential and you can see how it is a good model for such a phenomenon.

A good example of two variables that are inversely proportional to each other would be your time and average speed for a trip. Say you are driving a fixed distance. Then if you were to double your average speed, the total time would be cut in half, and vice versa. Any two variables that behave this way are said to be inversely proportional to each other.

Answer 4

Given two functions, a and b, a is the inverse of b if f(a)=1/f(b) and b is the inverse of a if f(b)=1/f(a).

An exponential decay function model would be radioactive decay, population decline, monetary depreciation, etc. The general formula is A(f) = A(i)[decay factor]^t where A(f) is the final amount, A(i) is the initial amount, decay factor is a number less than one (for example if the amount decreases at 10% per year, the decay factor is 0.9, and t is the time unit, usually years.

A function and its inverse will share some point (X,1)

Answer 5

Interesting!
the first exponential, is used to describe the decay- in this usage it means; causing to operate @3 times faster than the normal rate of decay.

inverse relationships- When you invert anything- for example a
glass, you turn it upside-down.( IE un-useful, you can not drink out of it in that state) Likewise the normal editifing relationship changes to negative and is predictable.

For example- Single parent who have no training often believe that it is their fault that their adolescent children are unwilling to co-operate. When the reverse is true, each and every one of us makes choices every single second, some are evident others are not that is our GOD GIVEN right. You see we are the only living creature that he gave self will too!! So inverse relationships would be the ones who encourage unhealthy, self defeating, self-destructive, esteem destroying interactions. Like the glass is made un-usable the relationship or interaction in it pushes you in directions you would NOT go by your self.

phase #1 starts of 3X faster than most and ends up dead!

phase #2 starts off negative and does not develop or produce anything you will be proud of.

Both are self- deceptive!
Both would describe the gang mentality, hope this helps!!

Answer 6

A function F is the inverse of a function G, if F is defined on the range of G and F(G(x)) = x . F(x) = exp x is the inverse of
G(x) = ln x

A function, F, decays exponentially as x goes to infinity if F(x) = A exp (-Bx) , B>0.