Question 1088726
formula is:

{{{F = P*e^(kt)}}} where:

{{{F}}} = future amount
{{{P}}} = present amount
{{{k }}}= constant of proportion.
{{{t}}} = time

half life of carbon is given by the equation:

{{{.5 = e^(5600k)}}} because:

half life of carbon is {{{5600}}} years.

solve for {{{k}}} and then you can solve the problem.

take log of both sides of equation of {{{.5 = e^(5600k)}}} to get:

{{{log(.5) = log(e^(5600k))}}}

this becomes:

{{{log(.5) = 5600k * log(e)}}}

divide both sides of this equation by {{{5600*log(e)}}} to get:

{{{k = log(.5)/(5600*log(e))}}}

solve for {{{k }}}to get:

{{{k = -.301029996 / (5600*.434294482)}}} which becomes:

{{{k = -.000123776 }}}


if the tree has only {{{73}}}%={{{0.73}}} of the carbon left, then your equation of: 

{{{F = P * e^(kt)}}} becomes:

{{{.73 = 1*e^(k*t)}}} which becomes:

{{{.73 = e^(-.000123776*t)}}}

take the log of both sides of this equation to get:

{{{log(.73) = log(e^(-.000123776*t))}}} which becomes:

{{{log(.73) = -.000123776*t*log(e)}}}

divide both sides of this equation by {{{-.000123776*log(e)}}} to get:

{{{t = log(.73) / (-.000123776*log(e))}}}

solve for {{{t}}} to get:

{{{t = 2542.58}}} years

Then round to the nearest whole number:{{{t = 2543}}} years