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