SOLUTION: Please help me solve this question: Complete the table for the radioactive isotope. (Round your answer to 2 decimal places.) Isotope is 14C Half Life is 5715 Initial Quantity is

Question 375944: Please help me solve this question: Complete the table for the radioactive isotope. (Round your answer to 2 decimal places.)
Isotope is 14C
Half Life is 5715
Initial Quantity is 21g
Find amount after 4000 years
Could you also show me how to solve the same equation if I was given the amount after 4000 years and I am trying to find the initial amount?
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
the mass is decreasing exponentially, giving half the mass at half-life tl :
m(t)=m0*exp(-at/tl), m(tl)=m0exp(-a)=m0/2 => a=ln(2)

m(t)=m0*exp(-ln(2)t/tl)
here t=4000, tl=5715, m0=21g,

m(4000)=21*exp(-ln(2)4000/5715)=21*0.6156=12.93g

let m=m0*exp(-ln(2)t/tl), find m0 :

m0=m*exp(ln(2)t/tl)
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