Carbon-14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for carbon-14 to decay to 10 percent of its original amount?

Question

wolf1728 · Answer

When is the percentage reduced to 10%?
Half Life of Carbon-14 = 5,730 years
Time = half-life * log(bgng amt/ending amt) / log2
Time = 5,730 * log (100%/10%) / 0.3010299957
Time = 5.730 years * 1/0.3010299957
Time = 19,034.65 years

I don't think radioactive decay occurs by percentage per year.  
.0124% = a factor of .000124 per year

That would mean after 8,065 years you are left with nothing?  No.  
After 5,730 years you are left with half
After 11,460 years you are left with .25 of what you started with
17,190	0.125
22,920	0.0625
28,650	0.03125
34,380	0.015625
40,110	0.0078125
45,840	0.00390625
51,570	0.001953125
57,300	0.0009765625

If radioactive decay occurred by .0124% per year, that would mean radioactive decay was an arithmetic function which it isn't.  It is a geometric function.

wolf1728 · Answer

Here is a webpage with a halflife calculator: http://www.1728.org/halflife.htm