document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202280>Question 1202280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At what point will f(x) = 3^x exceed g(x) = 2x + 5 and h(x) = x^2 +4?<BR>\n" );
document.write( "A. (x,y) = (1,7)<BR>\n" );
document.write( "B. (x,y) = (2.4, 9.8)<BR>\n" );
document.write( "C. (x,y) = (1.8, 3.7)<BR>\n" );
document.write( "D. (x,y) = (2,9) </SPAN>\n" );
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document.write( "Answer: Choice D<BR>\n" );
document.write( "(x,y) = (2,9)\r<BR>\n" );
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document.write( "Reason:<BR>\n" );
document.write( "Use a graphing calculator to find the approximate solution to 3^x = x^2+4 is x = 1.8<BR>\n" );
document.write( "Then 3^x = 3^(1.8) = 7.2 approximately<BR>\n" );
document.write( "F(x) exceeds h(x) at the point (1.8,7.2)\r<BR>\n" );
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document.write( "Use a graphing calculator to solve 3^x = 2x+5 and you should get x = 2 exactly<BR>\n" );
document.write( "3^x = 3^2 = 9<BR>\n" );
document.write( "2x+5 = 2*2+5 = 9<BR>\n" );
document.write( "f(x) exceeds g(x) at (2,9)\r<BR>\n" );
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document.write( "Graph comparing f(x) in green and g(x) in blue<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-2%2C4%2C-2%2C11%2C%0D%0Agraph%28400%2C400%2C-2%2C4%2C-2%2C11%2C-100%2C3%5Ex%2C2x%2B5%29%2C%0D%0Acircle%282%2C9%2C0.04%29%2C%0D%0Acircle%282%2C9%2C0.06%29%2C%0D%0Acircle%282%2C9%2C0.08%29%2C%0D%0Alocate%282-0.8%2C9%2B0.5%2C%22%282%2C9%29%22%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Graph comparing f(x) in green and h(x) in blue<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-2%2C4%2C-2%2C11%2C%0D%0Agraph%28400%2C400%2C-2%2C4%2C-2%2C11%2C-100%2C3%5Ex%2Cx%5E2%2B4%29%2C%0D%0Acircle%282%2C9%2C0.04%29%2C%0D%0Acircle%282%2C9%2C0.06%29%2C%0D%0Acircle%282%2C9%2C0.08%29%2C%0D%0A%0D%0Acircle%281.8%2C7.2%2C0.04%29%2C%0D%0Acircle%281.8%2C7.2%2C0.06%29%2C%0D%0Acircle%281.8%2C7.2%2C0.08%29%2C%0D%0A%0D%0Alocate%282-0.8%2C9%2B0.5%2C%22%282%2C9%29%22%29%2C%0D%0Alocate%281.8%2B0.1%2C7.2-0.1%2C%22%281.8%2C7.2%29%22%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "All three graphs together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-2%2C4%2C-2%2C11%2C%0D%0Agraph%28400%2C400%2C-2%2C4%2C-2%2C11%2C-100%2C3%5Ex%2C2x%2B5%2Cx%5E2%2B4%29%2C%0D%0Acircle%282%2C9%2C0.04%29%2C%0D%0Acircle%282%2C9%2C0.06%29%2C%0D%0Acircle%282%2C9%2C0.08%29%2C%0D%0Alocate%282-0.8%2C9%2B0.5%2C%22%282%2C9%29%22%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "f(x) = 3^x in green<BR>\n" );
document.write( "g(x) = 2x+5 in blue (straight line)<BR>\n" );
document.write( "h(x) = x^2+4 in purple (parabola)\r<BR>\n" );
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document.write( "Desmos and GeoGebra are two graphing apps I recommend.<BR>\n" );
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