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Element x decays radioactively with a half life of 9 minutes. If there are 850 grams of Element x, how long, to the nearest tenth of a minute, would it take the element to decay to 301 grams? y=a(.5)^

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Answer: The half life of the Element x is 9 minutes = 9x60 =540 seconds.

t(1/2) = 0.693/λ

λ = 0.693/540

λ = 0.00129

N = No.exponent(−λt)

where No is the mass of element at t = 0

and N is amount left

t is time

and λ is constant.

301 = 850 x exponential(-0.00129xt)

0.354 = exponential(-0.00129xt)

taking natural log both sides

ln(0.354) = (-0.00129 x t)

t = 805 seconds

805/60 = 13.42 minutes

Step-by-step explanation:

The half life time of any radioactive element is denoted by t(1/2) and is equal to 0.693/λ

and also to calculate the remaining amount after it decays for a time t is N = No.exponent(−λt)

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