document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200299>Question 1200299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The consumer price index compares the costs of goods and services over various years, where 1967 is used as a base. The same goods and services that cost $100 in 1967 cost $42 in 1940. Assuming the exponential-decay model<BR>\n" );
document.write( "(a) Estimate what the goods and services that cost $100 in 1967 cost in 1900. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834402 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=834402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general expnential growth formula is f = p * (1+r)^n<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "(1+r) is the growth factor per time period.<BR>\n" );
document.write( "r is the growth rate per time period.<BR>\n" );
document.write( "in this formula:<BR>\n" );
document.write( "f is the value in 1967<BR>\n" );
document.write( "p is the value in 1940<BR>\n" );
document.write( "n is equal to 1967 - 1940 = 27<BR>\n" );
document.write( "formula becomes 100 = 42 * (1+r)^27<BR>\n" );
document.write( "solve for (1+r) to get (1+r) = (100/42)^(1/27) = 1.032651381.<BR>\n" );
document.write( "that's your growth factor per year.<BR>\n" );
document.write( "that same growth factor per year applies to all years.<BR>\n" );
document.write( "when you want to know what the value was in 1900, the equation becomes:<BR>\n" );
document.write( "100 = p * 1.032651381 ^ 67<BR>\n" );
document.write( "solve for p to get:<BR>\n" );
document.write( "p = 100 / 1.032651381 ^ 67 = 11.61716321.<BR>\n" );
document.write( "that's the value of goods and services in 1900, based on the equation.\r<BR>\n" );
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document.write( "i don't know what formula you were given, so i'm at a loss to apply your fromula to get the answer, but the answer should be the same regardless if you used my formula or the formula you were given.\r<BR>\n" );
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document.write( "the formula i used can be graphed as shown below.\r<BR>\n" );
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document.write( "the formula in the graph is y = 100 / 1.032651381 ^ x\r<BR>\n" );
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document.write( "this is derived from f = p * (1+r)^n, where we solve for p to get:<BR>\n" );
document.write( "p = f / (1+r)^n<BR>\n" );
document.write( "in the graph, p is replaced by y and n is replaced by x and f is replaced by 100 to get:<BR>\n" );
document.write( "y = 100 / 1.032651381 ^ x\r<BR>\n" );
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document.write( "since i don't know what formula you were working from, i couldn't explain in that context.<BR>\n" );
document.write( "if you can provide me with the formula you were working from, i can work the problem using that formula.<BR>\n" );
document.write( "the answer should be the same.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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