document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=661979>Question 661979</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The yearly production of a 5 foot orange tree is 35 pounds of oranges. A 12 foot tree produces 54 pounds.<BR>\n" );
document.write( " What is the predicted production of an 18 foot tree?<BR>\n" );
document.write( "What is the predicted production of an 20 foot tree?<BR>\n" );
document.write( "What is the predicted height ( in feet ) of a tree that produces 88 pounds of oranges? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #411921 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=411921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the production, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > of an orange tree varies linearly with its height, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "we can write the linear equation that describes it, knowing two (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >) points.<BR>\n" );
document.write( "\"The yearly production of a 5 foot orange tree is 35 pounds of oranges,\" gives us point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35 ALIGN=MIDDLE  ALT=\"35\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "\"A 12 foot tree produces 54 pounds,\" gives us point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54 ALIGN=MIDDLE  ALT=\"54\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( " <BR>\n" );
document.write( "I can see 3 ways to get the answer.<BR>\n" );
document.write( "The expected way to solve the problem depends on what you are studying in class.<BR>\n" );
document.write( " <BR>\n" );
document.write( "CALCULATING SLOPE OF A LINE AND WRITING THE POINT-SLOPE FORM:<BR>\n" );
document.write( "We can calculate the slope, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the line:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%2854-35%29%2F%2812-5%29 ALIGN=MIDDLE  ALT=\"m=%2854-35%29%2F%2812-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=19%2F7 ALIGN=MIDDLE  ALT=\"m=19%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then we can use that slope and the coordinates of one of the points to write the equation in point-slope form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-35=%2819%2F7%29%28x-5%29 ALIGN=MIDDLE  ALT=\"y-35=%2819%2F7%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the point-slope form, we can go to the slope-intercept form, which will help answer the first 2 questions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-35=%2819%2F7%29%28x-5%29 ALIGN=MIDDLE  ALT=\"y-35=%2819%2F7%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-35=%2819%2F7%29x-5%2819%2F7%29 ALIGN=MIDDLE  ALT=\"y-35=%2819%2F7%29x-5%2819%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-35=%2819%2F7%29x-95%2F7 ALIGN=MIDDLE  ALT=\"y-35=%2819%2F7%29x-95%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2819%2F7%29x-95%2F7%2B35 ALIGN=MIDDLE  ALT=\"y=%2819%2F7%29x-95%2F7%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2819%2F7%29x-95%2F7%2B35 ALIGN=MIDDLE  ALT=\"y=%2819%2F7%29x-95%2F7%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2819%2F7%29x%2B150%2F7 ALIGN=MIDDLE  ALT=\"y=%2819%2F7%29x%2B150%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With a calculator, we can use the approximation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.714x%2B21.43 ALIGN=MIDDLE  ALT=\"y=2.714x%2B21.43\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and get accurate enough results.<BR>\n" );
document.write( "I'll stick with the fractions just in case you are expected to do that.<BR>\n" );
document.write( "For the 18 foot tree, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=18 ALIGN=MIDDLE  ALT=\"x=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2819%2F7%29%2A18%2B150%2F7 ALIGN=MIDDLE  ALT=\"y=%2819%2F7%29%2A18%2B150%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=342%2F7%2B150%2F7 ALIGN=MIDDLE  ALT=\"y=342%2F7%2B150%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=492%2F7=70%262%2F7 ALIGN=MIDDLE  ALT=\"y=492%2F7=70%262%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >=about<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70.29 ALIGN=MIDDLE  ALT=\"70.29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=about<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70 ALIGN=MIDDLE  ALT=\"70\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounding)<BR>\n" );
document.write( "I assume the expected answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70pounds ALIGN=MIDDLE  ALT=\"70pounds\"   DISABLED_style= \"max-width:90%; height:auto;\" > rounding to whole numbers.<BR>\n" );
document.write( "For the 20 foot tree,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=20 ALIGN=MIDDLE  ALT=\"x=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2819%2F7%29%2A20%2B150%2F7 ALIGN=MIDDLE  ALT=\"y=%2819%2F7%29%2A20%2B150%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=380%2F7%2B150%2F7 ALIGN=MIDDLE  ALT=\"y=380%2F7%2B150%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=530%2F7=75%265%2F7 ALIGN=MIDDLE  ALT=\"y=530%2F7=75%265%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >=about<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75.71 ALIGN=MIDDLE  ALT=\"75.71\"   DISABLED_style= \"max-width:90%; height:auto;\" >=about<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76 ALIGN=MIDDLE  ALT=\"76\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounding)<BR>\n" );
document.write( "I assume the expected answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76pounds ALIGN=MIDDLE  ALT=\"76pounds\"   DISABLED_style= \"max-width:90%; height:auto;\" > rounding to whole numbers.<BR>\n" );
document.write( "For the 88 pound production, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=88 ALIGN=MIDDLE  ALT=\"y=88\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=88=%2819%2F7%29x%2B150%2F7 ALIGN=MIDDLE  ALT=\"88=%2819%2F7%29x%2B150%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=88-150%2F7=%2819%2F7%29x ALIGN=MIDDLE  ALT=\"88-150%2F7=%2819%2F7%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=616%2F7-150%2F7=%2819%2F7%29x ALIGN=MIDDLE  ALT=\"616%2F7-150%2F7=%2819%2F7%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=466%2F7=%2819%2F7%29x ALIGN=MIDDLE  ALT=\"466%2F7=%2819%2F7%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying both sides times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=466%2F7=%2819%2F7%29x ALIGN=MIDDLE  ALT=\"466%2F7=%2819%2F7%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=466=19x ALIGN=MIDDLE  ALT=\"466=19x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=466%2F19=24%2610%2F19 ALIGN=MIDDLE  ALT=\"x=466%2F19=24%2610%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" >=about<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24.53 ALIGN=MIDDLE  ALT=\"24.53\"   DISABLED_style= \"max-width:90%; height:auto;\" >=about<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounding)<BR>\n" );
document.write( "I assume the expected answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25feet ALIGN=MIDDLE  ALT=\"25feet\"   DISABLED_style= \"max-width:90%; height:auto;\" > rounding to whole numbers.<BR>\n" );
document.write( " <BR>\n" );
document.write( "SETTING UP A SYSTEM OF EQUATIONS TO FIND SLOPE AND INTERCEPT:<BR>\n" );
document.write( "WE can find an equation of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=m%2Ax%2Bb ALIGN=MIDDLE  ALT=\"y=m%2Ax%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "by substituting the coordinates for out 2 points and solving the system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2854=12m%2Bb%2C35=5m%2Bb%29 ALIGN=MIDDLE  ALT=\"system%2854=12m%2Bb%2C35=5m%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving the system of equations leads to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=19%2F7 ALIGN=MIDDLE  ALT=\"m=19%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >=about<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.714 ALIGN=MIDDLE  ALT=\"2.714\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounding)<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=150%2F7 ALIGN=MIDDLE  ALT=\"b=150%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >=about<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21.43 ALIGN=MIDDLE  ALT=\"21.43\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounding)<BR>\n" );
document.write( "From that point on, the calculations are the same as done above.<BR>\n" );
document.write( " <BR>\n" );
document.write( "USING A COMPUTER/CALCULATOR AS IF IT IS A STATISTICS PROBLEM<BR>\n" );
document.write( "Using Excel functions in my computer, I can answer all 3 questions.<BR>\n" );
document.write( "With A1=5, A2=12, B1=35, B2=54,<BR>\n" );
document.write( "=FORECAST(18,B1:B2,A1:A2) gives me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70.29 ALIGN=MIDDLE  ALT=\"70.29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=492%2F7 ALIGN=MIDDLE  ALT=\"492%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%262%2F7 ALIGN=MIDDLE  ALT=\"70%262%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > pounds of oranges for an 18 foot tree.<BR>\n" );
document.write( "=FORECAST(20,B1:B2,A1:A2) gives me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75.71 ALIGN=MIDDLE  ALT=\"75.71\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=530%2F7 ALIGN=MIDDLE  ALT=\"530%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%265%2F7 ALIGN=MIDDLE  ALT=\"75%265%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > pounds of oranges for an 20 foot tree.<BR>\n" );
document.write( "=FORECAST(88,A1:A2,B1:B2) gives me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24.53 ALIGN=MIDDLE  ALT=\"24.53\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet for the height of a tree that would produce 88 pounds of oranges in a year. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );