document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203504>Question 203504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The consumer price index compares the cost of goods and services over various years. The same goods and services that cost $100 in 1967 cost $148.50 in 1977. Assuming exponential growth, find the value of these same goods and services in 1999.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "After what period of time did the same goods and services cost double that of 1967?<BR>\n" );
document.write( "Hint: x.xx years \r<BR>\n" );
document.write( "\n" );
document.write( "can someone help please<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153535 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=153535\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  The consumer price index compares the cost of goods and services over various years. The same goods and services that cost $100 in 1967 cost $148.50 in 1977. Assuming exponential growth, find the value of these same goods and services in 1999.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Let x=0 correspond to the year 1967.<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "Form::::::::: y = a*b^x<BR>\n" );
document.write( "(0,100):::: 100 = a*b^0<BR>\n" );
document.write( "(10,148.50):148.5= a*b^10<BR>\n" );
document.write( "---<BR>\n" );
document.write( "1st equation says a = 100<BR>\n" );
document.write( "Then b = 1.485^(1/10)<BR>\n" );
document.write( "--<BR>\n" );
document.write( "So the equation is y = 100 <BR>\n" );
document.write( "------------------------------------------<BR>\n" );
document.write( "find the value of these same goods and services in 1999.<BR>\n" );
document.write( "x = 1999-1967 = 32<BR>\n" );
document.write( "y = 100*(1.485^(3.2) = $354.43<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "After what period of time did the same goods and services cost double that of 1967?<BR>\n" );
document.write( "200 = 100(1.485^(x/10))<BR>\n" );
document.write( "---<BR>\n" );
document.write( "1.485^(x/10) = 2<BR>\n" );
document.write( "(x/10)log(1.485) = log(2)<BR>\n" );
document.write( "(x/10) = 1.753<BR>\n" );
document.write( "x = 17.53 years<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Year: 1967 + 17.53 = 1969 when rounded up.<BR>\n" );
document.write( "===============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );