Cesium 137 (Cs¹³⁷)is a Short-Lived Radioactive Isotope $e^{-\left(\frac{\ln 2}{30}\right) t}$ )As a Result of Its Operations, a Nuclear Power Plant

question 111

Multiple Choice

Cesium 137 (Cs¹³⁷) is a short-lived radioactive isotope.It decays at a rate proportional to the amount of itself present and has a half-life of 30 years (i.e., the amount of Cs¹³⁷ remaining t years after A₀ mg of the radioactive isotope is released is given by $e^{-\left(\frac{\ln 2}{30}\right) t}$ ) .As a result of its operations, a nuclear power plant releases Cs¹³⁷ at a rate of 0.12 mg per year.The plant began its operations in 1990, which we will designate as t = 0.Assume there is no other source of this particular isotope.Which of the following integrals give the total amount of Cs¹³⁷ T years after the plant began operations?

• A) \(\int_{0}^{T} e^{\left(-\frac{0.12 \ln 2}{30}\right) t} d t\)
• B) \(\int_{0}^{T} 0.12 e^{\left(-\frac{\ln 2}{30}\right) t} d t\)
• C) \(\int_{0}^{0.12} \ t e^{\left(-\frac{\ln 2}{30}\right) t} d t\)
• D) \(\left.\int_{0}^{T}\left(e^{\left(-\frac{\ln 2}{30}\right.}\right) t+0.12\right) d t\)

---

Definitions:

Asset Account

An account on a company's balance sheet that represents a resource with economic value owned or controlled by the business.

Revenue Accounts

Accounts that track the income generated from a company's primary and secondary activities, such as sales revenue, service revenue, and interest income.

Adjusting Entry

An adjusting entry is a journal entry made at the end of an accounting period to allocate income and expenditure to the period in which they actually occurred, ensuring the accounts reflect true and fair values.

Liability Account

An accounting ledger that shows the debts or obligations of a business, indicating amounts owed to creditors.