Question

10) The half-life of lodine-131 is 8 days. The initial amount is 20 milligrams. a) Find a function which gives the amount of lodine-131, Act), in milligrams, t days later. Round k, the decay constant, to four decimal places. b) Determine the length of time it takes for 70% of the material to decay. Round your answer to two decimal places. Be sure to label the answer.

Answer 1

Solved, using formula for Half life; Act) = do e-kut = 20 m.g. - e-k(8) Taking Ao= initial amount A= half life= 8 days :ACA) = 10 mg aften 8 days .: 10=20 e-k(8) + In both the sides -k(8) = ln (1) k=- ln (6) 8 k = 0.08 G64339 ~ 0.0866 : Our function Becomes Act) = 20 e -0.0866(A),

B Determine the length of time it takes for 70t. ach the material to Decay, ie Alt) = 0.70 Ao ACA) = 0.70 to Using Jurmalas Act) = Ao e 0.0866 Cut) 0.70= e-o. G8 GG (A) Taking in both the sides In (0.70) it 0.086G 4.1186 Et ie; No. of Days = 4:1186 days ~ 4.12 days Answer)