Question 1198954
b) The half-life of a radioactive substance is 300 years. If the initial amount is q milligrams, then the quantity q(t) remaining after t years is given by q(t) = q2^(kt). Find k
<pre>  {{{matrix(2,3, q(t), "=", q(2)^(kt), q(t)/q, "=", 2^(kt))}}} 
    {{{matrix(1,3, 1/2, "=", 2^(300k))}}} ----- Substituting {{{matrix(1,3, 1/2, for, q(t)/q)}}} and 300 for t
{{{matrix(1,3, 300k, "=", log (2, (1/2)))}}} ----- Converting to LOGARITHMIC form
 300k = - 1 ----- Substituting - 1 for {{{log (2, (1/2))}}}
  {{{highlight_green(matrix(1,3, k, "=", highlight((- 1)/300)))}}}</pre>