One of the byproducts of nuclear power generation is Uranium-233. Uranium is decaying at a constant 32% rate per day. If 12,880 pounds are produced from a power plant, what will the amount be in 20 days?

 To calculate the amount of Uranium-233 remaining after 20 days, given a decay rate of 32% per day, you can use the exponential decay formula, which is

\[ P(t) = P_0 \cdot e^{(-rt)} \]

where: - \( P(t) \) is the amount remaining after time \( t \), - \( P_0 \) is the initial amount, - \( r \) is the decay rate (expressed as a decimal), and - \( t \) is the time in days.

However, in this case, since we're dealing with a simple percentage per day and not a continuously compounded rate, we can use the formula:

\[ P(t) = P_0 \cdot (1 - r)^t \]

where: - \( P_0 \) is the initial amount (12,880 pounds), - \( r \) is the decay rate per day (32%, or 0.32 as a decimal), and - \( t \) is the time in days (20 days).

Let's calculate it:

\[ P(20) = 12,880 \cdot (1 - 0.32)^{20} \]

First, calculate \( (1 - 0.32) \):

\[ = 0.68 \]

Now raise 0.68 to the 20th power to see how much of the Uranium-233 remains after 20 days:

\[ 0.68^{20} \approx 0.01133 \] (this is an approximate value)

Lastly, multiply this value by the initial amount of Uranium-233 (12,880 pounds):

\[ P(20) \approx 12,880 \cdot 0.01133 \]

\[ P(20) \approx 145.9044 \] pounds (rounded to four decimal places)

So approximately 145.9 pounds of Uranium-233 will remain after 20 days, given a 32% decay rate per day.