document.write( "Question 256914: It is known that the mass, m(t), of a radio-active substance decreases as it decays, and that the equation governing this is m'(t)=-.005m(t) where t is in years. What is the half-life?\r
\n" ); document.write( "\n" ); document.write( "any help would be great!! \n" ); document.write( "

Algebra.Com's Answer #188952 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Half life means half of the original amount remains.
\n" ); document.write( " $\"dm%2Fdt=-0.005m\"$
\n" ); document.write( " $\"dm%2Fm=-0.005%2Adt\"$
\n" ); document.write( "Integrate,
\n" ); document.write( " $\"ln%28m%29=-0.005t%2BC\"$
\n" ); document.write( " $\"m=Ce%5E%28-0.005t%29\"$
\n" ); document.write( "where C=m0 when t=0, the original amount of material.
\n" ); document.write( " $\"m=m0%2Ae%5E%28-0.005t%29\"$
\n" ); document.write( "At $\"t=0\"$ , $\"m=m0\"$
\n" ); document.write( "When $\"t=t_h\"$ , $\"m=%281%2F2%29m0\"$
\n" ); document.write( "Substitute,
\n" ); document.write( " $\"%281%2F2%29m0=m0%2Ae%5E%28-0.005%28t_h%29%29\"$
\n" ); document.write( " $\"1%2F2=e%5E%28-0.005%28t_h%29%29\"$
\n" ); document.write( " $\"ln%281%2F2%29=-0.005%28t_h%29\"$
\n" ); document.write( " $\"t_h=%28ln%281%2F2%29%2F%28-%280.005%29%29%29\"$
\n" ); document.write( "t_h=138.6 years, approximately \n" ); document.write( "

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