Question 687656
 the half-life formula is:


{{{0.5 = e^(tk)}}}


{{{t = half-life_ time}}}


{{{k = decay constant}}}


Use what is given to find the {{{decay}}}{{{ constant}}}.


Given: 


half-life of silicon-32 is {{{710 years}}}


it means: {{{ t = 710}}}


Plug this into the equation.


{{{0.5 = e^(tk)}}}


{{{0.5 = e^(710k)}}}


Take the natural logs of both sides.


{{{ln(0.5) = ln e^710k}}}


{{{ln(0.5) = 710k}}}


{{{k = ln(0.5) / 710}}}


{{{k = -0.693147181 / 710}}}


{{{k = -0.000976263635}}}



{{{A = Pe^(kt)}}}


{{{A = ending_ amount}}} where


{{{P = starting_ amount}}}


{{{t = half-life _time}}}


{{{k = decay_ constant}}}



Plug in your known values.


{{{A = 40e^(-0.000976263635 *700)


{{{A = 40e^(-0.6833845445)}}}


{{{A = 40 * 0.5049052230}}}


{{{A = 20.19620892}}}



Rounded to three decimal places:


{{{A}}} ≈ {{{ 20.196g}}}


ANSWER: {{{ 20.196g}}}