You can model that you expect a 1.25% raise each year that you work for a certain company. if you currently make $50,000, how many years should go by until you are making $100,000?

  about 55.8

Step-by-step explanation:

The salary multiplier each year is 1.0125, so after n years, the salary has been multiplied by 1.0125^n.

We want to find the value of n that makes this multiplier be 2.

  2 = 1.0125^n

  log(2) = n·log(1.0125) . . . . . . . . . taking logs makes this a linear equation

  n = log(2)/log(1.0125) ≈ 55.8

The model predicts 55.8 years will go by until you are making $100,000.

More explanation of the factors used above

When 1.25% of s is added to s, the total is ...

  s + .0125s = s(1 +.0125) = 1.0125s . . . . . . the multiplier is 1.0125

__

After 2 years, the salary will be ...

  (s·1.0125)·1.0125 = s·1.0125²

After 3 years, the salary will be ...

  (s·1.0125²)·1.0125 = s·1.0125³

After n years, the salary will be ...

  s·1.0125^n

Estimate/Reasonableness check

The "rule of 72" tells you the doubling time in years is approximately 72/(annual percentage). For percentage = 1.25, this is ...

 doubling time ≈ 72/1.25 = 57.6 . . . years

This is in the neighborhood of the answer we calculated, so we conclude our answer is correct.