Plutonium-240 decays according to the function Q (t) = Q (subscripto) e^ (-kt) where Q represents the quantity remaining after t years and k is the decay constant, 0.00011 ... How long will it take 27 grams of plutonium-240 to decay to 9 grams? A.) 1.44 years B.) 18,900 years C.) 9,990 years D.) 2,100 years

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Mathematics

Paityn Joseph

27 September, 13:23

Plutonium-240 decays according to the function Q (t) = Q (subscripto) e^ (-kt) where Q represents the quantity remaining after t years and k is the decay constant, 0.00011 ... How long will it take 27 grams of plutonium-240 to decay to 9 grams? A.) 1.44 years B.) 18,900 years C.) 9,990 years D.) 2,100 years

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Lorenzo Blankenship · Answer 1

The answer is 9,990 years. Using the exponential decay question, we can figure out how long it will take Plutonium-240 to decay from 27 grams to 9 grams. Setting the equation up looks like this, 9 = 27 e^ (-0.00011 t). From this you get, 0.333333 = e ^ (-0.00011 t). Next, you simplify by dividing both sides by the natural log, - 1.0986 = - 0.00011 t. Finally, you solve by dividing both sides by - 0.00011, giving 9,987 years for t, rounded up to 9,990 years.