document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107512>Question 107512</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to help my daughter with her homework, but since I have no idea what I am doing I hope that having the answer will help me out:\r<BR>\n" );
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document.write( "Cricket Problem:  Based on information in Deep River Jim's Wilderness Trailbook, the rate at which crickets chirp is a lenear function of temperature.  At 55 degrees F they make 70 chirps per minute and at 69 degrees F they make 126 chirps per minute.<BR>\n" );
document.write( "a)  Write the equation expressing chirping rate as a function of temperature.<BR>\n" );
document.write( "b)  Predict the chirping rate at 90 degrees F.<BR>\n" );
document.write( "c)  How warm is it if they are chirping 120 chirps per minute?<BR>\n" );
document.write( "d)  Calculate the temperature-intercept.  What does this tell you about this numbeer in the real-world?<BR>\n" );
document.write( "e)  Calculate the chirping-intercept.  What does the chirping-intercept tell you about the real-worl?<BR>\n" );
document.write( "f)  Shetch and label the graph.\r<BR>\n" );
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document.write( "Thank you for any help.<BR>\n" );
document.write( "Brian </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78289 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=78289\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Linear equation means you need two points to calculate the equation. <BR>\n" );
document.write( "You have two points. <BR>\n" );
document.write( "Let C=chirp rate and T=temperature. <BR>\n" );
document.write( "The equation of a line is given by,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=mT%2Bb ALIGN=MIDDLE  ALT=\"C=mT%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where m is the slope of the line and b is the intercept. <BR>\n" );
document.write( "The slope is given by <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28T%5B2%5D-T%5B1%5D%29%2F%28C%5B2%5D-C%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m=%28T%5B2%5D-T%5B1%5D%29%2F%28C%5B2%5D-C%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the two data points, you gave,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28C%5B2%5D-C%5B1%5D%29%2F%28T%5B2%5D-T%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m=%28C%5B2%5D-C%5B1%5D%29%2F%28T%5B2%5D-T%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28126-70%29%2F%2869-55%29 ALIGN=MIDDLE  ALT=\"m=%28126-70%29%2F%2869-55%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=56%2F14 ALIGN=MIDDLE  ALT=\"m=56%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=4 ALIGN=MIDDLE  ALT=\"m=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the units are chirps per minute/degree F.<BR>\n" );
document.write( "You can solve for b by using m you just calculated and one data point. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=mT%2Bb ALIGN=MIDDLE  ALT=\"C=mT%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=4T%2Bb ALIGN=MIDDLE  ALT=\"C=4T%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126=4%2869%29%2Bb ALIGN=MIDDLE  ALT=\"126=4%2869%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126=276%2Bb ALIGN=MIDDLE  ALT=\"126=276%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126-276=276-276%2Bb ALIGN=MIDDLE  ALT=\"126-276=276-276%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-150 ALIGN=MIDDLE  ALT=\"b=-150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equation of your line is then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28T%29=4T-150 ALIGN=MIDDLE  ALT=\"C%28T%29=4T-150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can verify with your two points. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2855%29=4T-150 ALIGN=MIDDLE  ALT=\"C%2855%29=4T-150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2855%29=4%2855%29-150 ALIGN=MIDDLE  ALT=\"C%2855%29=4%2855%29-150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2855%29=220-150 ALIGN=MIDDLE  ALT=\"C%2855%29=220-150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2855%29=70 ALIGN=MIDDLE  ALT=\"C%2855%29=70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "70 chirps at 55 degrees F. That checks out. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2869%29=4T-150 ALIGN=MIDDLE  ALT=\"C%2869%29=4T-150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2869%29=4%2869%29-150 ALIGN=MIDDLE  ALT=\"C%2869%29=4%2869%29-150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2869%29=276-150 ALIGN=MIDDLE  ALT=\"C%2869%29=276-150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2869%29=126 ALIGN=MIDDLE  ALT=\"C%2869%29=126\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "126 chirps at 69 degrees F. That checks out. <BR>\n" );
document.write( "Your equation matches the data.<BR>\n" );
document.write( "a.)C(T)=4T-150 where C is chirps per minute, T is degrees F. <BR>\n" );
document.write( "Chirping rate at 90F.<BR>\n" );
document.write( "C(90)=4(90)-150<BR>\n" );
document.write( "C(90)=360-150<BR>\n" );
document.write( "C(90)=210<BR>\n" );
document.write( "b.)210 chirps per minute at 90 degrees F.<BR>\n" );
document.write( "C(T)=4T-150=120<BR>\n" );
document.write( "4T-150=120<BR>\n" );
document.write( "4T-150+150=120+150<BR>\n" );
document.write( "4T=270<BR>\n" );
document.write( "T=270/4<BR>\n" );
document.write( "c.)T=67.5 degrees F for 120 chirps per minute.\r<BR>\n" );
document.write( "\n" );
document.write( "d.) The temperature intercept is where the chirping rate is equal to zero. <BR>\n" );
document.write( "4T-120=0<BR>\n" );
document.write( "4T-120+120=120<BR>\n" );
document.write( "4T=120<BR>\n" );
document.write( "T=30 degrees F. <BR>\n" );
document.write( "In the real world, that says chirping doesn't start until 30 degrees.<BR>\n" );
document.write( "The birds are probably conserving their energy because its so cold. <BR>\n" );
document.write( "e.) The chirping intercept is where the temperature is equal to zero. <BR>\n" );
document.write( "C(0)=4(0)-120=-120.<BR>\n" );
document.write( "This doesn't really have a real world interpretation since there is no such thing as a negative chirp. Chirps need to be positive, that is not defined below T=30 degrees F. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+90%2C+-10%2C+190%2C+4x-120%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+90%2C+-10%2C+190%2C+4x-120%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );