11-13 11. -2 points SPreCalc7 4.6.019 This exercise uses the radioactive decay m

Question

11-13

11. -2 points SPreCalc7 4.6.019 This exercise uses the radioactive decay model The half-life of strontium-90 is 28 years. How long will t take a 100-mg sample to decay to a mass of 56 mg? ( ound your answer to the nearest whole number.) yr 12. 0/2 points 1 Previous Answers SPreCalc7 4.6 021.M This exercise uses the radioactive decay model If 250 mg of a radioactive element decays O s to 210 mg in 12 hours, find the half-life of the element. (Round your answer to the nearest w 12 hours, f Submit Answer Save Progress 13. -12 points SPreCalc7 4.6 022 This exercise uses the radioactive decay model After 3 days a sample of radon-222 has decayed to 58% of its original amount. a) What is the half-life of radon-2227 (Round your answer to two decimal places.) days (b) How long will it take the sample to decay to 30% of its original amount? (Round your answer to two decimal places.) days This exercise uses the radioactive decay model. A wooden artifact from an ancient tomb contains 70% of the carbon-1 whole number.) 4 that is present in living trees. How long ago was the artifact made? (The haif-life of carbon-14 is 5730 years. Round your decay ate s te O Type here to search

Explanation / Answer

11) standard exponential equation is given by

A = Ao e^kt

half life = 28 years

Ao/2 = Ao e^(28k )

k = ln (1/2) / 28

k = -0.024755

hence, equation is

56 = 100 e^ ( -0.024755 t )

56 / 100 = e^ ( -0.024755 t )

ln ( 56/ 100 ) =  -0.024755 t

t = 23

hence, it takes 23 years to decay

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