How many years would it take a 1000 gram sample to decay to only 300 grams

Question

The rate of decay for a particular type of radioactive particle is relatively constant, and can be represented using the equation

Where t is time, N is the mass of the sample, and 

 is the half-life (time it takes for half of the initial sample to decay).  The half-life of Carbon-14 is about 5730 years.  How many years would it take a 1000 gram sample to decay to only 300 grams?  Round your answer to the nearest tenth.

Answer 1

N(t)= 300 No =1000. N(t)/No= 300/1000=.3 and t 1/2 (half life) = 5730(-ln2)(t)/5739

.3 = e^(-ln2)(t)/5730. If we now take the natural log of both sides we gert

ln3 = (-ln2)(t)/5730

(5730)(ln3)= (-ln2)t

t= (5730)(ln3)/(-ln2). put this in your calculator and you get

t=9952.8

Remember when you take the natural log (ln) of e raised to some power the answer is whatever power e is raised to. This technique is needed to solve these sorts of equations

I hope this helps. The numbers are ugly but the principal is simple

Answer 2

Your answer would be 9952.8 years