Question

Prehistoric cave paintings were discovered in a cave in France. The paint contained 21% of the original carbon-14. Use the exponential decay model for carbon-14 A=AD -0.0001211 to estimate the age of the paintings The paintings are approximately years old. (Round to the nearest integer.)

Answer 1

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Solution II have exponential decay mode I A = -0.000121t Ao e Where t is time in years A = percentage of original carbon left (in decimal form) Ao = 100%. OT I we have, As 21 0.21 Ao Plug time =) Natural Value in above fomula to get -0.000121t 0.21 e Taking both side log In (0.21) = -(0.000121) t - to ln(0.21) -0.000121 -) -) t = 12898 Years. The paintings are approximately 12898 Years old

Solution! (2) know that half life of tranquilizer is 38 hours And would be exponential decay model o() A = Aol t 38 Where A is leta amount A.is indical amount 84 y. Decay amount a original amount = doo y Left amount (A) = 16. = 0.16 Intial Plug value in amount Ao = looy - 1 Volt above formula to get t in hours t -) 0.16 - 6) 38 =) Taking natural dog natural dog both side t -) In (0.10 ) In ( ² ) 38 -) 38 In (0.16 ) an (1/2) = t t ¢ 100.5 hours It will take hours 100.5 to decay 84 y. of original dosage