document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=668817>Question 668817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The annual consumption of frozen yogurt has decayed approximately exponentially from 2.6 pounds per person in 1995 to 1.0 pound per person in 2006. Predict when the consumption will be 0.5 pounds per person. Show steps.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #416090 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=416090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The annual consumption of frozen yogurt has decayed approximately exponentially<BR>\n" );
document.write( " from 2.6 pounds per person in 1995 to 1.0 pound per person in 2006.<BR>\n" );
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document.write( "Use the exponential decay formula using e<BR>\n" );
document.write( "Ao*e^(-t/k} = A, where <BR>\n" );
document.write( "Ao = initial amt<BR>\n" );
document.write( "A = resulting amt after t time<BR>\n" );
document.write( "t = time in yrs<BR>\n" );
document.write( "k = constant of decay of substance<BR>\n" );
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document.write( "t = 11 yrs (1995 to 2006)<BR>\n" );
document.write( "2.6*e^(-11/k) = 1<BR>\n" );
document.write( "Divide both sides by 2.6<BR>\n" );
document.write( "e^(-11/k) = .3846<BR>\n" );
document.write( "nat log of both sides (ln of e = 1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2Fk ALIGN=MIDDLE  ALT=\"-11%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ln(.3846)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2Fk ALIGN=MIDDLE  ALT=\"-11%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.9555<BR>\n" );
document.write( "k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-11%29%2F%28-.9555%29 ALIGN=MIDDLE  ALT=\"%28-11%29%2F%28-.9555%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "k = +11.512 is the constant of decay<BR>\n" );
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document.write( "Predict when the consumption will be 0.5 pounds per person.<BR>\n" );
document.write( "k = 11.512, find t<BR>\n" );
document.write( "2.6*e^(-t/11.512) = .5<BR>\n" );
document.write( "Divide both sides by 2.6<BR>\n" );
document.write( "e^(-t/11.512) = .1923<BR>\n" );
document.write( "Nat logs of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F11.512 ALIGN=MIDDLE  ALT=\"-t%2F11.512\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1.6487<BR>\n" );
document.write( "t = -1.6487 * -11.512<BR>\n" );
document.write( "t ~ 19 yrs from 1995; 2014, the year when consumption is only .5 lb </SPAN>\n" );
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