Question

lodind - 123 is a radioactive isotope of iodine and used for the diagnostic study of thyroid diseases. This substance decays by 5.1% every hour. Suppose you start with 50 mg of this substanceA) what is the decay factor per hour? Round decimal to three placesB) Write a formula that gives the remainingamount of lodine-123, A = A(t), measured in milligrams, after t hours.C) Calculate the half-life of lodine-123 by finding how long it will take for this substance to become half of its originalamount. Round decimal to two places

Answer 1

Given

50 mg of the substance

decay rate is 5.1% every hour

5.1 × 50 ÷ 100 = 2.55

So every hour the substance decays 2.55 mg

Given 2.55 mg is decayed after t hours

We start with 50 mg of lodine

A = 50

A = 50 - 2.55t

50 - 2.55 = 47.45 = 44.9 = 42.35 = 39.8=37.25=34.7 etc... + 4 additional hours

It takes 10 hours for the lodine to reach 24.5

24.5 rounded is 25