document.write( "Question 569464: 123=500e^-0.12x \n" ); document.write( "

Algebra.Com's Answer #367442 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Assume the problem is:
\n" ); document.write( " $\"123=500e%5E%28-0.12x%29\"$
\n" ); document.write( "rewrite it
\n" ); document.write( " $\"500e%5E%28-0.12x%29\"$ = 123
\n" ); document.write( "divide both sides by 500
\n" ); document.write( " $\"e%5E%28-0.12x%29\"$ = $\"123%2F500\"$
\n" ); document.write( " $\"e%5E%28-0.12x%29\"$ = .246
\n" ); document.write( ":
\n" ); document.write( "Using nat logs
\n" ); document.write( " $\"ln%28e%5E%28-0.12x%29%29\"$ = ln(.246)
\n" ); document.write( ":
\n" ); document.write( "the log equiv of exponents
\n" ); document.write( "-.12x*ln(e) = ln(.246)
\n" ); document.write( ";
\n" ); document.write( "find $\"e%5Ex\"$ of both sides, the nat log of e is 1
\n" ); document.write( "-.12x = -1.4024
\n" ); document.write( ";
\n" ); document.write( "x = $\"%28-1.4024%29%2F%28-.12%29\"$
\n" ); document.write( "x = +11.6869
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "We can check this on a good calc: enter 500*e^(-.12*11.6869). results 122.999 ~ 123 \n" ); document.write( "

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