document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=682835>Question 682835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a problem I can not figure out. In 1975, Visalia had a population of 65,000. In 2000 the population was 99,500. Assuming exponential growth, estimate the population in the 2015. Use A=A0e^kt </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #423371 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=423371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=A%5B0%5De%5Ekt ALIGN=MIDDLE  ALT=\"A=A%5B0%5De%5Ekt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=A%5B0%5De%5E%28k%2A0%29 ALIGN=MIDDLE  ALT=\"A=A%5B0%5De%5E%28k%2A0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=A%5B0%5De%5E0 ALIGN=MIDDLE  ALT=\"A=A%5B0%5De%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=A%5B0%5D%2A1 ALIGN=MIDDLE  ALT=\"A=A%5B0%5D%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=A%5B0%5D ALIGN=MIDDLE  ALT=\"A=A%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B0%5D ALIGN=MIDDLE  ALT=\"A%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the population at whatever time we decide to take as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=o ALIGN=MIDDLE  ALT=\"t=o\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Taking 1975 as time zero, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=year-1975 ALIGN=MIDDLE  ALT=\"t=year-1975\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is a good choice.<BR>\n" );
document.write( "In 1975, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1975-1975=0 ALIGN=MIDDLE  ALT=\"t=1975-1975=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "Visalia had a population of 65,000, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=A%5B0%5D=65000 ALIGN=MIDDLE  ALT=\"A=A%5B0%5D=65000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can write the exponential function as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=65000e%5Ekt%29 ALIGN=MIDDLE  ALT=\"highlight%28A=65000e%5Ekt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "but we still have to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "In 2000, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2000-1975=25 ALIGN=MIDDLE  ALT=\"t=2000-1975=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and the population was 99,500,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=65000e%5E25k=99500 ALIGN=MIDDLE  ALT=\"A=65000e%5E25k=99500\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E25k=99500%2F65000 ALIGN=MIDDLE  ALT=\"e%5E25k=99500%2F65000\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25k=ln%2899500%2F65000%29 ALIGN=MIDDLE  ALT=\"25k=ln%2899500%2F65000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%281%2F25%29ln%2899500%2F65000%29 ALIGN=MIDDLE  ALT=\"k=%281%2F25%29ln%2899500%2F65000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=0.0170308%29 ALIGN=MIDDLE  ALT=\"highlight%28k=0.0170308%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded approximation)<BR>\n" );
document.write( "Now we can write the exponential function as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=65000e%5E%280.0170308t%29%29 ALIGN=MIDDLE  ALT=\"highlight%28A=65000e%5E%280.0170308t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "In the year 2015, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2015-1975=40 ALIGN=MIDDLE  ALT=\"t=2015-1975=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and we estimate<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=65000e%5E%280.0170308%2A40%29 ALIGN=MIDDLE  ALT=\"A=65000e%5E%280.0170308%2A40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=65000e%5E0.681232 ALIGN=MIDDLE  ALT=\"A=65000e%5E0.681232\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=65000%2A1.976311 ALIGN=MIDDLE  ALT=\"A=65000%2A1.976311\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=128460%29 ALIGN=MIDDLE  ALT=\"highlight%28A=128460%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );