Calc II problem - depreciation of a machine?

Question

Hi - I need help with the following even question from my textbook:

A company buys a machine for $225,000 that depreciates at a rate of 30% per year. Find a formula for the value of the machine after n years. What is its value after 5 yrs.?

Any help would be appreciated. Thank-you!

Answer 1

At the end of 1 year, the value is $225,000*0.7 = $157,500
At the end of 2 years, the value is $157,500*0.7 = $110,250 = $225,000*(0.7)²
At the end of 3 years, the value is $110,250*0.7 = $77,175 = $225,000*(0.7)³

Value V(n) at the end of n years is

V(n) = 225000*(0.7)^n