document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173281>Question 173281</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0536941491/algebrahomeworkh>introduction to college mathematics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> First-class postage (for the first ounce) was 20cent in 1981 and 37cent in 2002.  Assume the cost increases according to an exponential growth function.\r<BR>\n" );
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document.write( "a. Let t =0 correspond to 1981 abd t= 21 correspond to 2002.  Then t is the number of years since 1981.  Use the data points (0,20) and (21,37) to find   the exponential growth rate and fit and exponential growth function <BR>\n" );
document.write( "P(t)= P0e ^kt to the data where P(t) is the cost of first-class postage, in cents, t years after 1981. <BR>\n" );
document.write( "b.  Use the function found in part (a) to predict the cost of first-class postage in 2008.<BR>\n" );
document.write( "c.  When will the cost of first-class postage be $1.00 or 100cent </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128124 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=128124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First-class postage (for the first ounce) was 20cent in 1981 and 37cent in 2002. Assume the cost increases according to an exponential growth function. <BR>\n" );
document.write( "a. Let t =0 correspond to 1981 abd t= 21 correspond to 2002. Then t is the number of years since 1981. Use the data points (0,20) and (21,37) to find the exponential growth rate and fit and exponential growth function <BR>\n" );
document.write( "P(t)= Poe ^kt to the data where P(t) is the cost of first-class postage, in cents, t years after 1981.<BR>\n" );
document.write( "Using the point (0,20)<BR>\n" );
document.write( "20 = Po*e^(k*0)<BR>\n" );
document.write( "20 = Po<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Now P(t) = 20*e^(kt)<BR>\n" );
document.write( "Using (21,37<BR>\n" );
document.write( "37 = 20e^(k*21)<BR>\n" );
document.write( "1.85 = e^(21k)<BR>\n" );
document.write( "21k = ln(1.85)<BR>\n" );
document.write( "k = (1/21)*0.6152<BR>\n" );
document.write( "k = 0.0293<BR>\n" );
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document.write( "Now P(t) = 20*e^(0.0293t)<BR>\n" );
document.write( "=================================== <BR>\n" );
document.write( "b. Use the function found in part (a) to predict the cost of first-class postage in 2008.<BR>\n" );
document.write( "1981 to 2008 = 27<BR>\n" );
document.write( "P(27) = 20*e^(0.0293*27) = 44.12<BR>\n" );
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document.write( "c. When will the cost of first-class postage be $1.00 or 100cent<BR>\n" );
document.write( "100 = 20e^(0.0293t)<BR>\n" );
document.write( "e^(0.0293t) = 5<BR>\n" );
document.write( "0.0293t = ln5<BR>\n" );
document.write( "t = 54.93<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "1981 + 54.93 = 2035.93<BR>\n" );
document.write( "Ans: $1.00 in the year 2036<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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