Exponential time decay - please help.

[f8l_0e]

Full disclosure: I am no mathematician. The furthest I got in high school was Algebra 2.

 

One of my favorite movies is The Manhattan Project. I want to build a prop replica of the device is the movie. I even plan to build the circuitry with discrete logic instead of a microcontroller. In the film, the device malfunctions due to radiation and its timer circuit begins to count down from 999h:99m:99s. The countdown increases exponentially. I would like to know the time to zero starting from 999:99:99 and possibly graph the decay rate over time.

 

In the film, the formula "As y approaches infinity t = (1 + (1 over / n ))to the nth." Some google-fu leads me to info on Euler's number.

 

 

Could someone assist with the formula needed to find the decay rate and the formula needed to calculate time remaining based on input?

 

Thanks,

 

John

[Sensei]

I have explained half-life calculation in this thread

http://www.scienceforums.net/topic/83245-a-question-on-radioactive-decay/?p=806204

 

You can simply use that Spread Sheet with your data.

 

current=start*2^(-time)

will give the same result as:

current=start*e*(-time*ln(2))

[f8l_0e]

Thank you for replying, Sensei. Forgive my ignorance, but I need some further hand holding. Can I just plug in the start time in seconds into the Current Quantity Of Elements column of the spreadsheet, or does the formula need to be rewritten?

 

 

[Sensei]

In that SpreadSheet you shouldn't play with first column where is time.

At least not until you will understand whole equation.

You change initial quantity (C2) and half-life (B2) fields.

Columns D,E will be filled automatically, and graph updated.

 

For f.e. half-life 10 seconds, and initial quantity 1000, you will see 1000,933,870,812,etc. going down quickly.

Edited June 24, 2014 by Sensei