Age of Seashell: Calculating 14-C Half Life

[matt222]

Homework Statement

seashell HAVE 90% of 14-C as a livining shell of the same size half life is 5570 years, how old is it in years

how many yrs did it take for 14-C to diminish from its initial value to 99% of that?

Homework Equations

The Attempt at a Solution

for the first part of problem 90% N0=N0exp(-kt), where k is decay constant from this k=1.24x10^-4
so t=847 years

for the second part of the problem we have the same decay constant k, so 99%N0=N0exp(-kt)

so for t I got t=81.1years

I think the first part is ok but i am not sure i about the second one

 

[Delphi51]

Looks good to me. Is your 3 digit accuracy for k sufficient? If I were you, I would keep about 5 digit accuracy because exponent accuracy strongly affects the accuracy of the power.

 

[matt222]

but it confused me the second part I am not sure about it 81 years compared to 847 years

 

[Delphi51]

I get 80.8 rather than 81.1, keeping all the digits on my calculator until rounding the final answer. You don't say what you are confused about. If you mean losing 1% in one tenth the time it loses 10%, that seems almost too reasonable to be true. Normally you can't trust your intuition on non-linear functions. It might be worth graphing the decay function on your calculator or computer to see if the function is fairly linear in that range.