half-life are given. Assume that it decays according to the formula A(t)-Aort wh
ID: 3116048 • Letter: H
Question
half-life are given. Assume that it decays according to the formula A(t)-Aort where Ais the initial amount of the material and k is the decay constant Cobalt 60, used in food irradiation, initial amount 500 grams, half-life of 5.27 years Find the decay constant k. Round your answer to four decimal places. Find a function which gives the amount of isotope A which remains after time t. (Keep the units of A and t the same as the given data.) A(r) Determine how ong it takes for 80% of the material to decay. Round your answer to two decimal places (HINT. If B09, of the material decays, how much S left?)Explanation / Answer
initial amount = 500
half life = 5.27 years
finding decay constant
A = Ao e^ kt
500/2 = 500 e^k(5.27)
ln 1/2 = k (5.27)
k = -0.1315
formula is
A = 500 e^ (-0.1315t )
c) time it takes for 80% of the matrial to decay
0.8 * 500 = 500 e^ (-0.1315t )
t = 1.70
it takes 1.7 years to decay
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