document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154750>Question 1154750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me answer this question:\r<BR>\n" );
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document.write( "The number N of tourists visiting a city in the t-th year after 2010 can be represented by the following formula:\r<BR>\n" );
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document.write( "       N = 114000 + 100000log(t+1)\r<BR>\n" );
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document.write( "It is given that the number of tourists in the t-th year is increased by 8000 when compared with that in the previous year.\r<BR>\n" );
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document.write( "(a) Will the number of tourists visiting the city per year be more than 214000 after 2019? \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 #777255 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=777255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula is N = 114000 + 100000 * log(T + 1)<BR>\n" );
document.write( "T is equal to 0 in the year 2010.<BR>\n" );
document.write( "T is equal to 9 in the year 2019.<BR>\n" );
document.write( "you want to know if the number of tourists visiting the city per year will be greater than 214000 after 2019.<BR>\n" );
document.write( "the formula for year 2019 is:<BR>\n" );
document.write( "N = 114000 + 100000 * log(9 + 1).<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "N = 114000 + 100000 * log(10).<BR>\n" );
document.write( "solve for N to get:<BR>\n" );
document.write( "N = 214000.<BR>\n" );
document.write( "the formula for year 2020 is:<BR>\n" );
document.write( "N = 114000 + 100000 * log(10 + 1)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "N = 114000 + 100000 * log(11)<BR>\n" );
document.write( "solve for N to get:<BR>\n" );
document.write( "N = 218139.2685<BR>\n" );
document.write( "that is greater than 214000, so the answer to question (a) is yes.<BR>\n" );
document.write( "the fly in the ointment her is the statement that it is given that the number of tourists in the year represent by t is 8000 when compared with that in the previous year.<BR>\n" );
document.write( "this is not true because the formula is not linear and therefore the increase in the number of tourists each year will not be the same.<BR>\n" );
document.write( "i graphed the equation by making N = y and T = x.<BR>\n" );
document.write( "you can see from the graph that the increase in the number of tourists between 2019 and 2020 is not 8000.<BR>\n" );
document.write( "the graph is shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/033001.jpg\" alt=\"$$$\" > </SPAN>\n" );
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