Question

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?

Answer 1

Approximately 0.0121 will be left after 15 days.

Explanation:

We can write an exponential function to model the situation. The standard exponential function is given by:

`y=a(b)^x`

Let x represent the amount of days. Since the initial amount is 3,820 pounds, a = 3820. It decays at a rate of 57% per day. So, after one day, it will only have 100% - 57% = 43% or 0.43 of its previous amount. So, b = 0.43.

Hence, our function is:

`y=3820(0.43)^x`

After 15 days, x = 15. Substitute and evaluate:

`y(15)=3820(0.43)^(15)\approx 0.0121\text{ pounds}`