You & Linear's claim is just like claiming interest compounded annually = interest compounded weekly merely because you can take the annual rate and backtrack it to any given week and produce a result. The results will not be the same, and anyone who really cares can find out for themselves. This isn't hard at all.
This too is a false statement, but more to the point, it demonstrates that either:
(a) CTD does not understand the math (does not understand that he is wrong), or
(b) CTD is incapable of admitting that he is wrong.
Let's use CTD's example of interest rates and see if this helps. When you calculate the ratio of interest to principal for one week (and anyone can take this problem to their local bank to have them verify it) you don't calculate it at 1/52 x the annual rate (what CTD did on the decay curve) but at the annual rate ^(1/52). Curiously when you do this you will also get the same curve as using an annual rate to graph interest versus time.
For simplicity let's calculate the interest due at 21% annual interest compounded annually and compounded semiannually on $100:
(1) compounded annually:
At the beginning of one year you have $100.00
At the end of the first year you have 1.21 x $100.00 = $121.00
(2) compounded semi-annually:
Calculating the interest rate to compound at 1/2 year (Nt/No)^1/2 = (121/100)^1/2 = 1.10
At the beginning of one year you have $100.00
At the end of 1/2 year you have 1.10 x $100.00 = $110.00
At the end of one year (two half years) you have 1.10 x $110.00 = $121.00
You can do the same for 1/3 years, 1/4 years, or 1/277 years, however no matter what interval you pick the annual interest rate will be the same, and the results will be the same curves.
Certainly this fact of interest calculations should be a part of high-school education that everyone should learn, as it directly affects your everyday life, so there is no rational excuse for not knowing this.
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