document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112025>Question 112025</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0201793873/algebrahomeworkh>Essentials of using and understanding mathematics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Doubling time formula. Use the approximate doubling time formula in exercise. Be sure to discuss whether the formula is valid for the case described.\r<BR>\n" );
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document.write( "20. Oil consumption is increasing at a rate of 1.9% per year. What is its doubling time? By what factor will oil consumption increase in a decade? </SPAN>\n" );
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document.write( "20. Oil consumption is increasing at a rate of 1.9% per year. What is its doubling time? By what factor will oil consumption increase in a decade?<BR>\n" );
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document.write( "The doubling time formula: A = Ao[2^(t/d)] <BR>\n" );
document.write( "where<BR>\n" );
document.write( "Ao is the initial amt<BR>\n" );
document.write( "A = resulting amt<BR>\n" );
document.write( "t = time<BR>\n" );
document.write( "d = doubling time<BR>\n" );
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document.write( "I don't think this formula will do the job; we don't know t or d:<BR>\n" );
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document.write( "How about 2 = 1(1+.019)^t, similar to the compound interest formula<BR>\n" );
document.write( "or just<BR>\n" );
document.write( "1.019^t = 2<BR>\n" );
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document.write( "t*ln(1.019) = ln(2)<BR>\n" );
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document.write( ".0188217t = .63147<BR>\n" );
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document.write( "t = .63147/.0188217<BR>\n" );
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document.write( "t = 36.8 years to double<BR>\n" );
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document.write( "Check it on a calc: enter: 1.019^36.8 = 1.99899 ~ 2<BR>\n" );
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document.write( "By what factor will oil consumption increase in a decade?<BR>\n" );
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document.write( "Since you know the doubling time (d) and t,  you can use the doubling formula<BR>\n" );
document.write( "A = 1[2^(10/36.8)<BR>\n" );
document.write( "A = 2^.2717<BR>\n" );
document.write( "A = 1.2072 is the factor for amt in a decade<BR>\n" );
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document.write( "Hope this helps you.<BR>\n" );
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