document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096558>Question 1096558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please check if I did this right?\r<BR>\n" );
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document.write( "A machine is now worth $159,500 an will be depreciated linearly over a 9 years period, at which time it will be worth $43,760 as scrap. <BR>\n" );
document.write( "a) Find the rule of depreciation function f?<BR>\n" );
document.write( "b) What is the domain of f?<BR>\n" );
document.write( "c) What will the machine be worth in 5 years?<BR>\n" );
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document.write( "a) f(x)=-115,740x+159,500<BR>\n" );
document.write( "b) Domain should be from 0, 159500 to ??? (I don't know)<BR>\n" );
document.write( "c)I used this formula: y=mx+b<BR>\n" );
document.write( "First, I found m= 43,760-159,500/9-0=-115,740/9==12,860<BR>\n" );
document.write( "Then  y= - 12, 860(5)+159,500=-95,200 <BR>\n" );
document.write( "Is it -95,200 correct result? I'm not sure. Thank you for your help and explanation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #710985 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=710985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>Let's look at your answer for part c first.<br><BR>\n" );
document.write( "You correctly found the slope by dividing the change in value by the number of years; the slope is -12,860.  That means the value is decreasing by $12,860 each year.  Then you found out how much the value would decrease over a 5 year period, and you subtracted that amount from the original value.  Exactly right.<br><BR>\n" );
document.write( "So you are good on part c.<br><BR>\n" );
document.write( "Now go back to part a.  The function you show suggests that the entire depreciation occurs in 1 year.  What you want in your function is the slope you calculated in part c.  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-12860x+%2B+159500 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-12860x+%2B+159500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Note that this is the standard \"y=mx+b\" form of the equation.  It is called standard form because it is the form that makes it easiest to use the equation in calculations.  But for a final answer to a question like this, a better form might be<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+159500+-+12860x ALIGN=MIDDLE  ALT=\"f%28x%29+=+159500+-+12860x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "because then it is easier to see that the meaning of the function is that the initial value if $159,500 and then the value decreases by $12,860 each year.<br><BR>\n" );
document.write( "And finally part b.<br><BR>\n" );
document.write( "Note that the domain is the set of x values, not the set of y (function) values.  Since the problem says the machine is considered scrap after 9 years, the domain is from 0 to 9.<br><BR>\n" );
document.write( "The answer you tried to give for this part is the range (set of y values).  And again, since the machine is considered scrap after 9 years, the range would be from $43,760 to $159,500, not 0 to $159,500.<br><BR>\n" );
document.write( "And technically, in mathematics when we state the range, we always go from lowest y value to highest, as in the previous paragraph.  But in this problem, speaking informally, it would make sense to say the range is from 159,500 to 43,760. </SPAN>\n" );
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