Question

PLEASE

Answer 1

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:

$P(t) = P(0)(1-r)^{t}$

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 $r = 0.12$, so

$P(t) = P(0)(1-r)^{t}$

$P(t) = P(0)(1-0.12)^{t}$

$P(t) = P(0)(0.88)^{t}$

By what percentage has Dan's car depreciated after 6 years?

Relative to the initial value, the value after 6 years is given by:

$P(6) = P(0)(0.88)^6 = 0.46P(0)$

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.