Answer:
y= 50,000(1-.075)^x
Step-by-step explanation:
The first year of depreciation is calculated by:
50,000 - (0.075)*(50,000) = 46,250
This can also be written as:
(50,000)*(1 - 0.075) [Pull out the 50,000]
The second year will depreciate starting with the $46,250 value at the end of the first year:
46,250 - (0.075)*(46,250) = 42,781
This may be written as:
(46,250)(1 - 0.075) = 42,781
The 46,250 was derived from the first year depreciation calculation, so we can substitute that instead of the 46,250:
((50,000)*(1 - 0.075))(1 - 0.075) = 42,781
This reduces to:
(50,000)*(1 - 0.075)^2 = 42,781. Note that the term (1-0.075) is now raised to the 2nd power. This power represents the 2nd year. Each succeeding year would be raised by one additional power, so that we can write a depreciated value after x years will be:
(50,000)*(1 - 0.075)^x
