document.write( "Question 1187783: Find the half-life of a certain radioactive substance which decays according to the
\n" ); document.write( "formula 𝑦 = 100𝑒
\n" ); document.write( "−3𝑡
\n" ); document.write( ", where y is the amount present after t years?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #818825 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "Find the half-life of a certain radioactive substance which decays according to the formula 𝑦 = \"100%2Ae%5E%28-3t%29\",
\n" ); document.write( "where y is the amount present after t years?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "The initial mass is 100 units at t= 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "At the half-life value of t,  the remaining mass is  \"100%2F2\" = 50.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we write the decay equation in  ekt-form\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    50 = \"100%2Ae%5E%28-3t%29\"\r\n" );
document.write( "\r\n" );
document.write( "    \"50%2F100\" = \"e%5E%28-3t%29\"\r\n" );
document.write( "\r\n" );
document.write( "    0.5 = \"e%5E%28-3t%29\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Take logarithm base \"e\"  (natural logarithm) of both sides\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "   ln(0.5) = -3t\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Express \"t\" and calculate\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    t = \"ln%280.5%29%2F%28-3%29\" = 0.231049  years.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  \"100%2Ae%5E%28-3%2A0.231049%29\" = \"100%2A2.71828%5E%28-3%2A0.231049%29\" = use your calculator = 50.0000    ! precisely correct !\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On radioactive decay,  see the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Radioactive decay problems \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You will find many similar  (and different)  solved problems there.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        Use this lesson as your handbook,  textbook,  guide,  tutorials, and  (free of charge)  home teacher.\r
\n" ); document.write( "\n" ); document.write( "        Learn the subject from there once and for all.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in  ALGEBRA-I  in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Logarithms\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );