Thanks, Bex.

So you openly condemn CTD's frequent ad hominem comments to anyone that disagrees with him. Good to see, and I'm sure that others, LindaLou, Russel2, LinearAq, and especially Pwwca will appreciate this even-handed condemnation.

We are, however, talking about math, the "perfect science" according to some, and which has nothing to do with belief. It is relatively easy to show that you are either right or not when doing math.

The math we are talking about here, of course, is a simple exponential equation:

Nt = No*e^(-?t)

Where
Nt = The amount of material at a particular time
No = The initial amount of material.
t = The time expended
? = the decay rate, which is differs between materials

... and where ? does not change depending on what time of year you use it in a formula, but stays constant.

As pointed out, CTD made a mistake when he calculated his "quarter-life" as half of a "half-life" and then compounded his error when he claimed that the value of the curve at his half of a half-life was a linear interpolation between the value at time "o" to the value at time "t" ... a claim that is obviously false because the curve is ... curved, not a straight line.

The inescapable truth is that CTD is either wrong about how long a "quarter-life" is OR he is wrong about the value of the curve at his mis-defined point. The inescapable truth is that he is wrong, period. There is no gray in math calculations.

Now, instead of simply admitting that he was wrong, CTD tries to hide the fact by first substituting a different formula for the decay curve. As we have seen this new formula is for interest calculations based on a nominal (read approximate) initial rate:

A = P(1 + (r/n)}^{nt}

Where
* P = principal amount (initial investment)
* r = annual nominal interest rate (as a decimal)
* n = number of times the interest is compounded per year
* t = number of years
* A = amount after time t

Now to compare these two formulas we can restate the decay formula with the symbols used in the interest rate formula:

A = P*e^(rt)

* P = Initial amount (No)
* r = annual rate (positive for growth, negative for decay)
* t = number of years
* A = amount after time t (Nt)

Now when we compare these two formulas we notice

(1) that there is no "n" factor in the actual decay curve
(2) that (1 + (r/n)} does not equal e
(3) that (1 + (r/n)} varies with n while e is constant
(4) that (nt) does not equal (rt)

If that does not convince anyone that CTD is lying about the curves being equivalent (which is what he is claiming when he says you can substitute on for the other when making your calculations) then consider this:

(a) When you ask your banker what the real rate of interest is, he will tell you (if he is an honest banker) that it is the APR rate, not the nominal rate. This means that any calculation for interest to compare with decay you would have to use the same APR rate (and as noted previously, that when you do that you get the same results, ones that are still not CTD's results.

(b) The formula used for compound calculations is a relatively easy to use approximation of a constant growth curve.

When you look at your bank statements for an account compounded annually with an APR of 8.24% and a $100 initial investment you will see:

Starting Deposit: $100.00
End of month 1: $100.00
End of month 2: $100.00
End of month 3: $100.00
End of month 4: $100.00
End of month 5: $100.00
End of month 6: $100.00
End of month 7: $100.00
End of month 8: $100.00
End of month 9: $100.00
End of month 10: $100.00
End of month 11: $100.00
End of month 12: $108.24
(end of year = 1 compound period)
End of month 13: $108.24
End of month 14: $108.24
End of month 15: $108.24
etc etc etc

One does not even need to graph this to show that it is not a curve function but a step function.

When you look at your bank statements for an account compounded quarterly with an APR of 8.24% (and the quarterly rate 2.00% - see the wiki "A" conversion example) and a $100 initial investment you will see:

Starting Deposit: $100.00
End of month 1: $100.00
End of month 2: $100.00
End of month 3: $102.00
(end of 1st 1/4 = 1 compound period)
End of month 4: $102.00
End of month 5: $102.00
End of month 6: $104.04
(end of 2nd 1/4 = 2 compound periods)
End of month 7: $104.04
End of month 8: $104.04
End of month 9: $106.12
(end of 3rd 1/4 = 3 compound periods)
End of month 10: $106.12
End of month 11: $106.12
End of month 12: $108.24
(end of year = 4 compound periods)
End of month 13: $108.24
End of month 14: $108.24
End of month 15: $110.41
etc etc etc

Even when you correctly use the same APR rate for the comparison to decay curves, it is still a step function and not a smooth curve as is given by the decay formula.

The decay formula is actually easier to use (fewer inputs, fewer calculation steps), and thus the whole substitution of one formula for another does not accomplish a correct calculation nor does it make it easier to calculate. For instance you can use one of these on-line calculators:

http://www.bioscience.org/urllists/decay.htm (three fields to enter data: half-life, amount, time).

enter 1000 (years), 100 (percent), 1000 (years) and it calculates the amount remaining at 50 (percent)

enter 1000 (years), 100 (percent), 500 (years) and it calculates the amount remaining at 70.71067811865476(percent)

Which, curiously, is the square root of 1/2 as a percent value. This is the true amount for any decay curve at half of a half-life. So once again CTD cannot be right when he claims the value is 75%. Wrong is wrong.

Can we refer you to this statement whenever a creationist decides that they have been insulted? Fair is fair eh?

Enjoy.