Question 1157950
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An equation of the radioactive decay in this case is 


    {{{C*(1/2)^(t/5730)}}} = {{{0.62*C}}},


where C is the initial mass of carbon-14 in the sample; t is the time in years.


Simplify and solve for "t", which is the major unknown in this case.

Start canceling "C" in both sides.


    {{{(1/2)^(t/5730)}}} = 0.62


Take logarithm base 2 from both sides


    -t/5730 = {{{log(2,(0.62))}}}


    -t/5730 = -0.6897


    t = 5730*0.6897 = 3952 years    (rounded to closest integer value).      <U>ANSWER</U>
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