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One of the byproducts of nuclear power generation is Uranium-233. Uranium is decaying at a constant 57% rate per day. If 3,820 pounds are produced from a power plant, what will the amount be in 15 days?



A.) 19,737,001.91

B.) 19,737,001

C.) 0.739

Verified Answer :

C because if you subtract 57 from 100, you get 43. Then you take the total amount of Uranium and multiply it by 43 15 times you get 0.739

Answer:

C) 0.739

Step-by-step explanation:

We have been given Uranium-233 is decaying at a constant 57% rate per day. There were 3,820 pounds of Uranium-233 produced from a power plant.

To find the amount of uranium left after 15 days we will use continuous exponential decay function.  

\(y=a*e^{-kt}\), where,

a = Initial amount,

e = Mathematical constant,

k = A number representing decay rate in decimal form.

t = Time.

Let us convert our given rate in decimal form.

\(57\%=\frac{57}{100}=0.57\)

Upon substituting our given values in above formula we will get,

\(y=3,820*e^{-0.57*15}\)

\(y=3,820*e^{-8.55}\)

\(y=3,820*0.0001935450995581\)

\(y=0.739342280311942\approx 0.739\)

Therefore, the amount of Uranium-233 after 15 days will be 0.739 pounds and option C is the correct choice.

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