The local parts shop buys a machine that costs $500000. its value depreciates exponentially each year by 10%. What is the machine's value after 5 years? round your answer to the nearest integer.
The value of the machine after each year can be found using the formula V = Vo(1 - r)^t, where V is the value after t years, Vo is the initial value, and r is the depreciation rate per year. In this case, Vo = $500000 and r = 10% = 0.1.
After 1 year:
V = $500000(1 - 0.1)^1 = $450000
After 2 years:
V = $500000(1 - 0.1)^2 = $405000
After 3 years:
V = $500000(1 - 0.1)^3 = $364500
After 4 years:
V = $500000(1 - 0.1)^4 = $328050
After 5 years:
V = $500000(1 - 0.1)^5 = $295245.
Therefore, the machine's value after 5 years is approximately $295245. Rounded to the nearest integer, the answer is $295245.