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  • Radioactive Decay Calculation: Determining Remaining Substance Over Time
    To determine the amount of radioactive substance remaining after a certain number of years, we can use the following formula:

    \(A = A_0 * (1 - r)^t\)

    Where:

    * \(A\) is the amount of radioactive substance remaining after time t

    * \(A_0\) is the initial amount of radioactive substance

    * \(r\) is the decay rate per year

    * \(t\) is the time in years

    In this case, we have:

    * \(A_0\) = 700 milligrams

    * \(r\) = 8.8% = 0.088

    * \(t\) = number of years

    To find the amount of radioactive substance remaining after 1 year, we plug these values into the formula:

    \(A = 700 * (1 - 0.088)^1\)

    \(A = 700 * 0.912\)

    \(A = 638.4 milligrams\)

    So, after 1 year, there will be 638.4 milligrams of radioactive substance remaining.

    To find the amount of radioactive substance remaining after 2 years, we plug these values into the formula:

    \(A = 700 * (1 - 0.088)^2\)

    \(A = 700 * 0.829\)

    \(A = 579.3 milligrams\)

    So, after 2 years, there will be 579.3 milligrams of radioactive substance remaining.

    We can continue this process to find the amount of radioactive substance remaining after any number of years.

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