Question

(1 point) The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-ife of 5543 years. Suppose C(t) is the amount of carbon-14 present at time t. (a) Find the value of the constant k in the differential equation C"=-kC k= (b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material[1]. How was old the Shroud of Turin in 1988, according to these data? Age = years [1]: The New York Times, October 18, 1988.

Answer 1

lat Tnftia amont of is o Hals lise ime 5543 yay s c-ke kt dekc dt ekd n ()-k() te Te CFnkgahon Gonchut CCヒ=り543) = Cct-o) Then -k(5543 Co e うe lan (2)-0.000 135 1 こ0.0001つち七 91 (00 = -0.000125 t -O.09431--0.00025 y t=0943) Oc000125 t1154.48 21 eass