document.write( "Question 1144147: We have three pay levels. Level 1 employees begin at $15,000. The notes say that in the third year the salary should rise to $19,000. Level 2 employees start at $30,000 and according to the notes, their salary should rise to $36,000 in year 3. Finally, Level 3 employees start at $50,000 and the notes say that they should be making $58,000 by the end of year 3. The only other piece of information I have is that the growth of salary over time is supposed to follow a linear growth pattern - whatever that means.\r
\n" ); document.write( "\n" ); document.write( "The notes also say that once a Level 1 employee has worked long enough to reach a salary of $30,000 he or she should either be promoted to Level 2 or fired. The same applies to Level 2 employees when they reach $50,000 in salary. Can you help me out? I need first to know what exactly is the rate of increase for each level of employee over time. I would also like a mathematical model that will allow me to input the number of years the employee has been working for us and give back their current salary.\r
\n" ); document.write( "\n" ); document.write( "Finally, I would like to know after how many years of working for us a Level 1 employee should expect to be promoted to Level 2 and after how many years of working for us can a Level 2 employee be promoted to a Level 3.
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Algebra.Com's Answer #765158 by Theo(13342)\"\" \"About 
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linear growth rate means the same number of dollar increases each year.\r
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\n" ); document.write( "\n" ); document.write( "level 1 starts at 15000 in year 1 and reaches 19000 in year 3.
\n" ); document.write( "that's a growth rate of 2000 per year.\r
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\n" ); document.write( "\n" ); document.write( "level 2 starts at 30000 in year 1 and reaches 36000 in year 3.
\n" ); document.write( "that's a growth rate of 3000 per year.\r
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\n" ); document.write( "\n" ); document.write( "level 3 starts at 50000 in year 1 and reaches 58000 in year 3.
\n" ); document.write( "that's a growth rate of 4000 per year.\r
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\n" ); document.write( "\n" ); document.write( "this is like an arithmetic progression.
\n" ); document.write( "formula is An = A1 + (n-1) * d\r
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\n" ); document.write( "\n" ); document.write( "for level 1, formula becomes An = 15000 + (n-1) * 2000
\n" ); document.write( "for level 2, formula becomes An = 30000 + (n-1) * 3000
\n" ); document.write( "for level 3, formula becomes An = 50000 + (n-1) * 4000\r
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\n" ); document.write( "\n" ); document.write( "n represents the year.\r
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\n" ); document.write( "\n" ); document.write( "for level 1, you get:
\n" ); document.write( "A1 = 15000
\n" ); document.write( "A2 = 17000
\n" ); document.write( "A3 = 19000
\n" ); document.write( "etc.\r
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\n" ); document.write( "\n" ); document.write( "for level 2, you get:
\n" ); document.write( "A1 = 30000
\n" ); document.write( "A2 = 33000
\n" ); document.write( "A3 = 36000
\n" ); document.write( "etc.\r
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\n" ); document.write( "\n" ); document.write( "for level 3, you get:
\n" ); document.write( "A1 = 50000
\n" ); document.write( "A2 = 54000
\n" ); document.write( "A3 = 58000\r
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\n" ); document.write( "\n" ); document.write( "to find out when level 1 reaches 30000, the formula becomes:
\n" ); document.write( "30000 = 15000 + (n-1) * 2000
\n" ); document.write( "subtract 15000 from both sides of that equation to get:
\n" ); document.write( "15000 = (n-1) * 2000
\n" ); document.write( "divide both sides of that equation by 2000 to get:
\n" ); document.write( "15000 / 2000 = n-1
\n" ); document.write( "simplify to get 7.5 = n-1
\n" ); document.write( "solve for n to get n = 8.5\r
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\n" ); document.write( "\n" ); document.write( "to find out when level 2 reaches 50000, the formula becomes:
\n" ); document.write( "50000 = 30000 + (n-1) * 3000
\n" ); document.write( "subtract 30000 from both sides of that eqution to get:
\n" ); document.write( "20000 = (n-1) * 3000
\n" ); document.write( "divide both sides of that equation by 3000 to get:
\n" ); document.write( "20000 / 3000 = n-1
\n" ); document.write( "simplify to get 6 + 2/3 = n-1
\n" ); document.write( "solve for n to get n = 7 + 2/3\r
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\n" ); document.write( "\n" ); document.write( "level 1 reaches 30000 salary halfway between the 8th year and the 9th year.\r
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\n" ); document.write( "\n" ); document.write( "level 2 reaches 50000 salary two thirds of the way between the 7th and 8th year.\r
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