Question

The value of an industrial machine has a decay factor of 0.75 per year. After six years, the machine is worth $7,500. What was the original value of the machine?

Answer 1

If the value was initially v, then after a year it is 0.75v, after 2 years it’s 0.75²v, and so on. So after 6 years it’s 0.75⁶v.
So 0.75⁶v=7500, and v=7500/0.75⁶=$42,139.92 approximately. This is close to $42,140.