Question

question: a radioactive compound with mass 260 grams decays at a rate of 3.8% per hour. which equation represents how many grams of the compound will remain after 8 hours? answer: c = 260(1.038)^8, c = 260(0.962)^8, c = 260(0.038)^8, c = 260(1 - 0.38)^8

Explanation:

Step1: Find the decay factor

The compound decays at a rate of 3.8% per hour. The decay - factor is \(1 - 0.038=0.962\) since if the rate of decay is \(r = 3.8\%=0.038\), the remaining fraction of the compound after each hour is \(1 - r\).

Step2: Use the exponential - decay formula

The general formula for exponential decay is \(C = C_0(1 - r)^t\), where \(C_0\) is the initial amount, \(r\) is the rate of decay, and \(t\) is the time. Here, \(C_0 = 260\) grams, \(r = 0.038\), and \(t = 8\) hours. Substituting these values into the formula, we get \(C = 260(0.962)^8\).

Answer:

\(C = 260(0.962)^8\) (second option)