Exponential decay function

[jones12345]

Which formulation of equations fits the following behavior, so that a factor decreases from 1 to 0 and they all approach the same x-value in the end?
(1) exponential type decay (green)
(2) linear decrease type (black)
(3) inverse exponential type decay (red)

I think that I have found an expression for the first 2:
(1) y = exp(-b*x), however for small values of b the factor does not approach y = 0
(2) y = -bx + 1
(3) I don't know...

Thanks!

 

[Deleted member 4993]

Which formulation of equations fits the following behavior, so that a factor decreases from 1 to 0 and they all approach the same x-value in the end?
(1) exponential type decay (green)
(2) linear decrease type (black)
(3) inverse exponential type decay (red)
Thanks!
View attachment 30763

What are your thoughts? Please be explicit.

 

[jones12345]

What are your thoughts? Please be explicit.

Hi, thanks for the reply! I have added some of my thoughts

 

[Dr.Peterson]

Which formulation of equations fits the following behavior, so that a factor decreases from 1 to 0 and they all approach the same x-value in the end?
(1) exponential type decay (green)
(2) linear decrease type (black)
(3) inverse exponential type decay (red)

I think that I have found an expression for the first 2:
(1) y = exp(-b*x), however for small values of b the factor does not approach y = 0
(2) y = -bx + 1
(3) I don't know...

Thanks!
View attachment 30763

It isn't clear what you mean by "a factor decreases from 1 to 0", but you seem to mean what happens to y as x increases from 0 to some value.

The problem with (1) is that exponential decay never actually reaches zero. There is no "in the end"! The green graph could be an exponential decay with a negative asymptote, or something else entirely, like a cycloid.

You are right about (2), as long as you can determine the value of b so that it reaches zero at the right value of x.

I don't know what "inverse exponential type decay" means! Is this a term you learned somewhere? The red graph can be expressed as exponential growth flipped upside down, or more generally as y = 1 - f(a - x), where f is the red function. Can you use that idea to find an equation that fits it?

Where did this question come from? If it's your own personal question, how was the graph made?