Every year the valur of a surveying machine depreciates by 25% of its value in the previous year. If the value of the machine was $11250 in 2012, find its value in 2010.

backing up 2 years,

11250/(.75)^2 = 20,000

what is 11250(.75)^2 ?

I want step by step

To find the value of the surveying machine in 2010, we need to work backwards from 2012, applying the annual depreciation rate of 25%.

Let's denote the value of the machine in 2012 as V2012 = $11,250.

Since the machine depreciates by 25% each year, the value of the machine in 2011 (V2011) can be calculated by multiplying the value in 2012 by (1 - 0.25):

V2011 = V2012 * (1 - 0.25)
V2011 = $11,250 * 0.75
V2011 = $8,437.50

Following the same logic, the value of the machine in 2010 (V2010) would be:

V2010 = V2011 * (1 - 0.25)
V2010 = $8,437.50 * 0.75
V2010 = $6,328.13

Therefore, the value of the surveying machine in 2010 is approximately $6,328.13.