QuestionMay 4, 2025

6. A sample contains 1 gram of Ruthenium-106 which has a half-life of one year. 6a Write a function, A , to represent the amount of the sample remaining after n years. Enteryournextstephere

6. A sample contains 1 gram of Ruthenium-106 which has a half-life of one year. 6a Write a function, A , to represent the amount of the sample remaining after n years. Enteryournextstephere
6. A sample contains 1 gram of Ruthenium-106 which has a half-life of one year. 6a Write a function, A , to represent the amount of the sample remaining after n years. Enteryournextstephere

Solution
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Answer

A(n) = (0.5)^n Explanation 1. Define the decay formula The amount remaining after n years follows the exponential decay formula: A(n) = A_0 \cdot (0.5)^n, where A_0 is the initial amount and n is the number of years. 2. Substitute initial values Given A_0 = 1 gram, the function becomes A(n) = 1 \cdot (0.5)^n.

Explanation

1. Define the decay formula<br /> The amount remaining after $n$ years follows the exponential decay formula: $A(n) = A_0 \cdot (0.5)^n$, where $A_0$ is the initial amount and $n$ is the number of years.<br /><br />2. Substitute initial values<br /> Given $A_0 = 1$ gram, the function becomes $A(n) = 1 \cdot (0.5)^n$.
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