Question 1162581
The half-life of a radioactive material is about 34.3 years. How much of a 1-gram sample of the material is left after 20 years? (Round your answer to four decimal places.)
<pre>Continuous GROWTH/DECAY formula: {{{matrix(1,3, A, "=", A[o]e^(kt))}}}
If half-life (.5-life) is 34.3 years, then DECAY CONSTANT, or {{{matrix(1,3, k, "=", ln(.5)/34.3)}}}
We then get: {{{matrix(1,3, A, "=", A[o]e^kt)}}}
             {{{matrix(1,3, A, "=", matrix(2,1, " ", 1e^((ln(.5)/34.3) * 20)))}}} ------- Substituting {{{matrix(3,3, 1, for, A[o], ln(.5)/34.3, for, k, 20, for, t)}}}
             Amount of the 1-gram material that remains after 20 years, or {{{highlight_green(matrix(1,6, A, "=", "0.667532332,", rounded, to, highlight(matrix(1,2, .6675, gram)))))}}}