SOLUTION: At the beginning of an experiment, a scientist has 308 grams of radioactive goo. After 150 minutes, her sample has decayed to 9.625 grams. What is the half-life of the goo in min

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Question 958536: At the beginning of an experiment, a scientist has 308 grams of radioactive goo. After 150 minutes, her sample has decayed to 9.625 grams.
What is the half-life of the goo in minutes?
How many grams of goo will remain after 5 minutes?
Answer by stanbon(75887) About Me  (Show Source):
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At the beginning of an experiment, a scientist has 308 grams of radioactive goo. After 150 minutes, her sample has decayed to 9.625 grams.
What is the half-life of the goo in minutes?
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A(t) = a*b^t
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9.625 = 308*b^150
0.03125 = b^(150)
b = 0.97716
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A(t) = 308*0.97716^t
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Solve::
0.95516^t = 1/2
t = ln(0.5)/ln(0.95516) = 30 minutes (that is the half-life)
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How many grams of goo will remain after 5 minutes?
A(t) = 308*0.97716^t
308*0.97716^300 = 0.30078 grams (amt. after 5 min)
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Cheers,
Stan H.
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Solve::
0.5^x = 0.97716
x = log(0.97716)/log(0.5) = 0.3333
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A(t) = 308*(1/2)