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Solution:
Formula for radioactive Decay is given by
= Initial Population
R = Remaining population after time in hours
Rate of Decay = S % per hour
Initial Population = 72 grams
Final population = 15 grams
Rate of Decay = 35 % per hour
Substituting the values to get value of t in hours
→→1 St expression
But taking positive value of t , that is after 3.64 hours the sample of 72 grams decays to 15 grams at the rate of 35 % per hour.
Now , it is also given that, Once the sample reaches a mass of 15 grams, Billy will continually add more of the compound to keep the sample size at a minimum of 15 grams.
Substituting these in Decay Formula
Final Sample = 15 gm
Starting Sample = 15 +k, where k is amount of sample added each time to keep the final sample to 15 grams.
Time is over 3.64 hours i.e new time = 3.64 + t
Rate will remain same i.e 35 % per hour.
→→→ Final expression (Second) , that is inequalities can be used to determine the possible mass of the radioactive sample over time.