Question 1144147
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.