document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157956>Question 1157956</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A midwestern city had a population of 650,000 in 2010. The population, which follows the exponential model, decreased 4.65% per year. Show all work!\r<BR>\n" );
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document.write( " a. Find the exponential function that models the population after t years.<BR>\n" );
document.write( " (Remember to change the rate to a negative decimal.)\r<BR>\n" );
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document.write( " b. What is the projected population in the year 2020?\r<BR>\n" );
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document.write( " c. In how many years will the population be expected to be 300,000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781981 by </B><A HREF=/tutors/aboutme.mpl?userid=Amily_2190><B>Amily_2190(27)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Amily_2190><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=781981\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)Population decreased 4.65% per year; -4.65%= -.0465<BR>\n" );
document.write( "To determine how much of the population remains per year, subtract 4.65%(-.0465) from the total population of 100% or 1. <BR>\n" );
document.write( "1-.0465=.9535<BR>\n" );
document.write( "t=# of years after 2010\r<BR>\n" );
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document.write( "Answer: P(t)= 650,000(.9535)^t \r<BR>\n" );
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document.write( "b) 2020-2010= 10 (2020 is 10 years after 2010, so t=10)<BR>\n" );
document.write( "P(t)=650,000(.9535)^10 is approximately 403,757\r<BR>\n" );
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document.write( "c) 300,000= 650,000(.9535)^t<BR>\n" );
document.write( "300,000/650,000=(.9535)^t<BR>\n" );
document.write( "(Use logarithm to figure out t on calculator)<BR>\n" );
document.write( "log base .9535 of 300,000/650,000 equals t\r<BR>\n" );
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document.write( "t is approximately 16.2 years<BR>\n" );
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