document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202756>Question 1202756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 2018, a 2-liter of Coca-Cola cost $1.40. In 2022, the cost is $1.98. <BR>\n" );
document.write( "Write an exponential equation to describe the rate of inflation over this time period. Let t = 0 correspond to 2018, and let C be the cost of a 2-liter. Round any numbers calculated to at least four decimal places.<BR>\n" );
document.write( "C = ?\r<BR>\n" );
document.write( "\n" );
document.write( "If inflation continues at the same rate, how much will a 2-liter of Coke cost in 2033? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837836 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=837836\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red size=4>$5.14</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Explanation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I'll use x in place of t, and y in place of C.<BR>\n" );
document.write( "x = t<BR>\n" );
document.write( "y = C\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "One template of an exponential function is<BR>\n" );
document.write( "y = a*b^x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 0 corresponds to the year 2018.<BR>\n" );
document.write( "When x = 0, the cost is y = 1.40<BR>\n" );
document.write( "The point (0,1.40) is on the exponential curve.<BR>\n" );
document.write( "It is the y intercept.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The gap from 2022 to 2018 is 4 years (since 2022-2018 = 4).<BR>\n" );
document.write( "x = 4 corresponds to the year 2022.<BR>\n" );
document.write( "We have x = 4 pair with y = 1.98<BR>\n" );
document.write( "The point (4,1.98) is also on the exponential curve.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plug in the coordinates of the 1st point.<BR>\n" );
document.write( "y = a*b^x<BR>\n" );
document.write( "1.40 = a*b^0<BR>\n" );
document.write( "1.40 = a*1<BR>\n" );
document.write( "1.40 = a<BR>\n" );
document.write( "a = 1.40<BR>\n" );
document.write( "This is the initial value.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have<BR>\n" );
document.write( "y = a*b^x<BR>\n" );
document.write( "update to<BR>\n" );
document.write( "y = 1.40*b^x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plug in the coordinates of the 2nd point<BR>\n" );
document.write( "y = 1.40*b^x<BR>\n" );
document.write( "1.98 = 1.40*b^4<BR>\n" );
document.write( "1.98/1.40 = b^4<BR>\n" );
document.write( "1.414286 = b^4<BR>\n" );
document.write( "b = (1.414286)^(1/4)<BR>\n" );
document.write( "b = 1.090522<BR>\n" );
document.write( "The result is approximate\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore,<BR>\n" );
document.write( "y = 1.40*b^x<BR>\n" );
document.write( "updates to<BR>\n" );
document.write( "y = 1.40*(1.090522)^x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Graph of y = 1.40*(1.090522)^x through the points (0,1.40) and (4,1.98)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-3%2C7%2C-5%2C5%2C%0D%0Agraph%28400%2C400%2C-3%2C7%2C-5%2C5%2C-100%2C1.40%2A%281.090522%29%5Ex%29%2C%0D%0Acircle%280%2C1.40%2C0.05%29%2Ccircle%280%2C1.40%2C0.1%29%2Ccircle%280%2C1.40%2C0.15%29%2Ccircle%284%2C1.98%2C0.05%29%2Ccircle%284%2C1.98%2C0.1%29%2Ccircle%284%2C1.98%2C0.15%29%2C%0D%0A%0D%0Alocate%280%2B0.3%2C1.40%2C%22%280%2C1.40%29%22%29%2C%0D%0Alocate%284%2B0.3%2C1.98%2C%22%284%2C1.98%29%22%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "GeoGebra and Desmos are two graphing options I recommend.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The year 2033 is 2033-2018 = 15 years after 2018.<BR>\n" );
document.write( "Plug in x = 15<BR>\n" );
document.write( "y = 1.40*(1.090522)^x<BR>\n" );
document.write( "y = 1.40*(1.090522)^(15)<BR>\n" );
document.write( "y = 5.13623051169986<BR>\n" );
document.write( "y = 5.14<BR>\n" );
document.write( "The two-liter coke is estimated to cost around <font color=red>$5.14</font> in the year 2033.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );