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.
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.
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.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! linear growth rate means the same number of dollar increases each year.
level 1 starts at 15000 in year 1 and reaches 19000 in year 3.
that's a growth rate of 2000 per year.
level 2 starts at 30000 in year 1 and reaches 36000 in year 3.
that's a growth rate of 3000 per year.
level 3 starts at 50000 in year 1 and reaches 58000 in year 3.
that's a growth rate of 4000 per year.
this is like an arithmetic progression.
formula is An = A1 + (n-1) * d
for level 1, formula becomes An = 15000 + (n-1) * 2000
for level 2, formula becomes An = 30000 + (n-1) * 3000
for level 3, formula becomes An = 50000 + (n-1) * 4000
n represents the year.
for level 1, you get:
A1 = 15000
A2 = 17000
A3 = 19000
etc.
for level 2, you get:
A1 = 30000
A2 = 33000
A3 = 36000
etc.
for level 3, you get:
A1 = 50000
A2 = 54000
A3 = 58000
to find out when level 1 reaches 30000, the formula becomes:
30000 = 15000 + (n-1) * 2000
subtract 15000 from both sides of that equation to get:
15000 = (n-1) * 2000
divide both sides of that equation by 2000 to get:
15000 / 2000 = n-1
simplify to get 7.5 = n-1
solve for n to get n = 8.5
to find out when level 2 reaches 50000, the formula becomes:
50000 = 30000 + (n-1) * 3000
subtract 30000 from both sides of that eqution to get:
20000 = (n-1) * 3000
divide both sides of that equation by 3000 to get:
20000 / 3000 = n-1
simplify to get 6 + 2/3 = n-1
solve for n to get n = 7 + 2/3
level 1 reaches 30000 salary halfway between the 8th year and the 9th year.
level 2 reaches 50000 salary two thirds of the way between the 7th and 8th year.
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