Question

You bought a car for $50,000. Each year it depreciates in value by 7.5%.

Answer 1

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