Comparing Decay Rates from Two Methods: Is α = β?

[lisab]

I’m going to post this here even though this question straddles Chemistry and Physics. I think I know the answer but I’d like confirmation.

Let's say I am measuring a property P that is decaying exponentially, but I am measuring it using two different test methods. Let’s call them method A and method B.

The data from method A fit the curve:

P(t) = A₀e^-αt

The data from method B fit the curve:

P(t) = B₀e^-βt

In this case, I know the methods well enough that I know that A₀ and B₀ will be different numbers. But isn’t it true that α = β?

 

[Borek]

If you are measuring the same property, but getting different results, something is wrong. And if something is wrong, everything can go wrong (that is, if A₀≠B₀, I don't see why to expect α=β).

Is it just an experimental error, or is there more to the difference between both methods?

 

[I like Serena]

If α = β, but A0<B0, then the first curve is less then the second curve everywhere.
In other words, they cannot fit the same data regardless of systematic or experimental errors.

Therefore, if A0≠B0 then that implies α≠β.

 

[lisab]

OK, mystery (sort of) solved.

Turns out there are two typos. One, the author accidentally used the same variable for the exponent. Two, in a graph showing results from both tests, there are supposed to be two sets of axes but only one got into the report.

I didn't notice the first typo but it was the graph that made my head spin. The units weren't right -- method A and method B give results in different units, so I was confused !

Thanks, Borek and ILS.