SOLUTION: At the beginning of an experiment, a scientist has 140 grams of radioactive goo. After 60 minutes, her sample has decayed to 2.1875 grams. What is the half-life of the goo in

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: At the beginning of an experiment, a scientist has 140 grams of radioactive goo. After 60 minutes, her sample has decayed to 2.1875 grams. What is the half-life of the goo in       Log On


   

Question 1159187: At the beginning of an experiment, a scientist has 140 grams of radioactive goo. After 60 minutes, her sample has decayed to 2.1875 grams.

What is the half-life of the goo in minutes?

Find a formula for G(t), the amount of goo remaining at time t. G(t)=

How many grams of goo will remain after 53 minutes?
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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Notice that  140%2F2.1875 = 64 = 2%5E6.


It means that 60 minutes comprise 6 half-life periods.



Thus one half-life period is   60%2F6 = 10 minutes.


Therefore, the formula for G(t)  is  G(t) = 140%2A%28%281%2F2%29%5E%28t%2F10%29%29,  where t is in minutes from the starting moment.


To answer the last question, substitute t= 53 into the formula


    G(53) = 140%2A0.5%5E5.3 = 3.553604 grams.

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Solved. All the questions are answered.