document.write( "Question 1104549: Please help me solve this word problem: in 1997, there were a total of 1,316,999 bankruptcies filed under the Bankruptcy Reform Act. The model for the number of bankruptcies filed is B(t)=0.798*1.164^t, where t is the number of years since 1994 and B is the number of bankruptcies filed in terms of millions (administrative office in US courts, statistical tables for the federal judiciary). In what year is it predicted that 12 million bankruptcies will be filed? \n" ); document.write( "
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\n" ); document.write( "Please help me solve this word problem: in 1997, there were a total of 1,316,999 bankruptcies filed under the Bankruptcy Reform Act. The model for the number of bankruptcies filed is B(t)=0.798*1.164^t, where t is the number of years since 1994 and B is the number of bankruptcies filed in terms of millions (administrative office in US courts, statistical tables for the federal judiciary). In what year is it predicted that 12 million bankruptcies will be filed?
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\n" ); document.write( " \"B%28t%29+=+0.798%281.164%29%5Et\"
\n" ); document.write( " \"12+=+0.798%281.164%29%5Et\" ---- Substituting 12 for B(t), the number of bankruptcies, in MILLIONS
\n" ); document.write( "\"12%2F0.798+=+%281.164%29%5Et\"
\n" ); document.write( " \"t+=+log+%281.164%2C+%2812%2F.798%29%29\" -- Converting to LOGARITHMIC form
\n" ); document.write( " t = 17.8488, approximately
\n" ); document.write( "With t representing TIME, in years, since 1994, we get the year that 12M bankruptcies
\n" ); document.write( "will be predicted to be filed as: 1994 + 17.8488, or 2011.8488, which is in the year 2011.
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