document.write( "Question 1027560: The half life of a specific radioactive compound is 15 years. The equation used to model this half-life is y=200(1/2)^t/15, where T represents time when 200 pounds of this substance remaining. Determine approximately how much of the substance remains after 82 years. Round to the nearest tenth of a year. \n" ); document.write( "

Algebra.Com's Answer #642778 by fractalier(6550) $\"\"$ $\"About$

You can put this solution on YOUR website!
To do this, we wish to find the time t, where y = 82, so
\n" ); document.write( "y=200(1/2)^t/15
\n" ); document.write( "82=200(1/2)^t/15
\n" ); document.write( ".41 = (1/2)^t/15
\n" ); document.write( "ln .41 = (t/15)ln(1/2)
\n" ); document.write( "-.8916 = (t/15)*-.6931
\n" ); document.write( "t/15 = 1.2863
\n" ); document.write( "t = 19.3 years \n" ); document.write( "

\n" );