Answer:
Dan's car depreciated by 54% after 6 years.
Step-by-step explanation:
Price of a depreciating asset:
The price of a depreciating asset after t years is given by:
[tex]P(t) = P(0)(1-r)^{t}[/tex]
In which P(0) is the initial price and r is the decrease rate, as a decimal.
Dan's car depreciates at a rate of 12% per year.
This means that [tex]r = 0.12[/tex], so
[tex]P(t) = P(0)(1-r)^{t}[/tex]
[tex]P(t) = P(0)(1-0.12)^{t}[/tex]
[tex]P(t) = P(0)(0.88)^{t}[/tex]
By what percentage has Dan's car depreciated after 6 years?
Relative to the initial value, the value after 6 years is given by:
[tex]P(6) = P(0)(0.88)^6 = 0.46P(0)[/tex]
The value after 6 years if 0.44 of the initial value, that is, there was a depreciation of 100 - 46 = 54%.
Dan's car depreciated by 54% after 6 years.
