Question 1161523
You could try a model like 
A, amount at time x
p, initial amount if x is 0
x, time passage in years
5730, the half-life of Carbon-14, in years

{{{A=p(1/2)^(x/5730)}}}


Question part (a) for "decay constant",  more like {{{A=pe^(-kx)}}}

{{{1/2=e^(-5730k)}}}

{{{ln(1/2)=-5730k}}}

{{{-ln(2)=-5730k}}}

{{{k=ln(2)/5730}}}

{{{highlight_green(k=0.0001210)}}}

(To the "tenth" decimal place makes no sense in the given example.)



Part (b):


Either model can be used.  

{{{system(p=1,A=29/50)}}}

{{{(1/2)^(x/5730)=29/50}}}

{{{(x/5730)*log((1/2))=log((29))-log((50))}}}

{{{x=(5730/log((1/2)))(log((29))-log((50)))}}}-------evaluate this.

( 4500 years ago)