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. 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

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.

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