Final answer:
The original value of the surveying machine in 2010, before it depreciated by 25 percent annually to reach $11250 in 2012, was $20000.
Step-by-step explanation:
Calculating the Original Value of a Surveying Machine
To find the value of a surveying machine in 2010, given its value in 2012 after annual depreciation of 25 percent, we must work backwards. If the machine was worth $11250 in 2012, we can use the formula for depreciation, V = P(1 - r)^n, where V is the final value, P is the original value, r is the depreciation rate (0.25), and n is the number of years. Since we are looking for the value in 2010, n would be negative because we are going back in time.
Applying the formula, the calculation for 2011 would be $11250 / (1 - 0.25), and doing the same for 2010, we get the value for 2010 as $11250 / (1 - 0.25)^2. Calculating this gives $11250 / 0.5625, which equals $20000. So, the surveying machine's original value in 2010 was $20000.