Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

math help explain?

The half-life of 14C is 5730 years. A chemist measures the amount of 14C in a bone tissue sample to be about 1/16th of the amount that was present when it died. About how many years ago did the animal die? 

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  • Alan
    Lv 7
    1 month ago

    A = A_0*(1/2)^(t/5730) 

    is A_0 is the original amount A/A_0 = (1/2)^(t/5730)  and you are saying  A/A_0 = 1/16   1/16 = (1/2)^(t/5730) take ln of both sides ln (1/16) =  (t/5730)ln(1/2) (t/5730) =  ln(1/16)/ln(1/2)   t = ln(1/16)*5730/ln(1/2)  = 22920   years 

    or alternatively 

    1/16 = (1/2)^(t/5730) 

    take log base 2  of both sides 

    log_b2(1/16)  =   (t/5730) log_b2(1/2)  

    -4  = (t/5730) * -1  

    -4/-1 = t/5730 

    t/5730 =4  

    t = 5730*4 =  22920 years 

  • alex
    Lv 7
    1 month ago

    1/16 = (1/2)^4

    time= 4 * 5730 =22920years

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