document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468861>Question 468861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My teacher gave me this problem to solve and I don't understand how to work it out. Need help<BR>\n" );
document.write( "Margarita is hired by an accounting firm at a starting salary of $58,000 per year.  Three years later her annual salary has increased to $66,400.  Assume her salary increases linearly.\r<BR>\n" );
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document.write( "a)  Write the equation of a linear function that relates her annual salary, S, and the number of years, t, she has worked for the firm.<BR>\n" );
document.write( "b)  What does the slope of her salary function represent?<BR>\n" );
document.write( "c)  What does the S-intercept of her salary function represent?<BR>\n" );
document.write( "d)  Assuming the same rate of growth, after how many years with the firm will her salary first exceed $100,000? Describe what you did to arrive at your result.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321689 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Margarita is hired by an accounting firm at a starting salary of $58,000 per year. Three years later her annual salary has increased to $66,400. Assume her salary increases linearly.<BR>\n" );
document.write( "a) Write the equation of a linear function that relates her annual salary, S, and the number of years, t, she has worked for the firm.<BR>\n" );
document.write( "b) What does the slope of her salary function represent?<BR>\n" );
document.write( "c) What does the S-intercept of her salary function represent?<BR>\n" );
document.write( "d) Assuming the same rate of growth, after how many years with the firm will her salary first exceed $100,000? Describe what you did to arrive at your result.<BR>\n" );
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document.write( "Starting Salary is $58,000<BR>\n" );
document.write( "She makes $66,400 in 3 years.<BR>\n" );
document.write( "Salary is increasing linearly (in a straight line).<BR>\n" );
document.write( "S = Salary<BR>\n" );
document.write( "T = number of years.<BR>\n" );
document.write( "her rate of growth is equal to (66,400 - 58,000) / 3 = $2,800 per year.<BR>\n" );
document.write( "Since the annual growth is in the form of a straight line equation, it will take the form of S = m*T + b<BR>\n" );
document.write( "m is the slope and b is the S intercept.<BR>\n" );
document.write( "The slope is the change in Salary per year which is equal to $2,800.<BR>\n" );
document.write( "the equation becomes:<BR>\n" );
document.write( "S = 2800*T + b<BR>\n" );
document.write( "The S intercept is the value of S when T = 0.<BR>\n" );
document.write( "When T = 0, she was just starting and her salary was $58,000, so the value of b is equal to $58,000.<BR>\n" );
document.write( "the equation becomes:<BR>\n" );
document.write( "S = 2800*T + 58000<BR>\n" );
document.write( "The * is the multiplication symbol.<BR>\n" );
document.write( "2800*T is equivalent to 2800 times T.<BR>\n" );
document.write( "The equation is S = 2800*T + 58000 as stated above.<BR>\n" );
document.write( "The questions can now be answered.<BR>\n" );
document.write( "They are:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a) Write the equation of a linear function that relates her annual salary, S, and the number of years, T, she has worked for the firm.<BR>\n" );
document.write( "S = 2800 * T + 58000<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "b) What does the slope of her salary function represent?<BR>\n" );
document.write( "It represents the change in salary each year.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "c) What does the S-intercept of her salary function represent?<BR>\n" );
document.write( "It represents her starting salary.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "d) Assuming the same rate of growth, after how many years with the firm will her salary first exceed $100,000? Describe what you did to arrive at your result.<BR>\n" );
document.write( "The equation is S = 2800 * T + 58000<BR>\n" );
document.write( "S will be equal to $100,000, so replace S with that figure in the equation to get:<BR>\n" );
document.write( "100000 = 2800 * T + 58000<BR>\n" );
document.write( "subtract 58000 from both sides of this equation to get:<BR>\n" );
document.write( "42000 = 2800 * T<BR>\n" );
document.write( "divide both sides of this equation by 2800 to get:<BR>\n" );
document.write( "T = 15.<BR>\n" );
document.write( "She will reach a salary of $100,000 per year in the 15th year of her employment.<BR>\n" );
document.write( "We can graph this equation, but we have to replace S with y and T with x in order to do that.<BR>\n" );
document.write( "the equation becomes:<BR>\n" );
document.write( "y = 2800 * x + 58000<BR>\n" );
document.write( "We'[ll graph that equation for 20 years out into the future.<BR>\n" );
document.write( "The graph of that equation is shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C20%2C-20000%2C130000%2C2800%2Ax%2B58000%2C58000%2C66400%2C100000%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C20%2C-20000%2C130000%2C2800%2Ax%2B58000%2C58000%2C66400%2C100000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I drew 3 horizontal lines at y = 58000 and y = 66400 and y = 100000 so you can spot the year in which those values occur easier.<BR>\n" );
document.write( "just grace a vertical line down from the intersection of those horizontal lines with the line of the equation to get an approximate estimate of the year in which they occur.<BR>\n" );
document.write( "the year should be 0, 3, and 15 which can be confirmed easily by replacing x in the equation with 0, 3, and 15, and solving for y.<BR>\n" );
document.write( "Note the equation is the same:<BR>\n" );
document.write( "S = 2800 * T + 58000 is exactly the same equation as:<BR>\n" );
document.write( "y = 2800 * x + 58000.<BR>\n" );
document.write( "Only the names have been changed to protect the innocent.\r<BR>\n" );
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