Question

in the year 2001, a person bought a new car for $15500. for each consecutive year after that, the value of the car depreciated by 5%. how much would the car be worth in the year 2005, to the nearest hundred dollars?

Explanation:

Step1: Define depreciation formula

The value of an asset with annual depreciation follows the formula:
$$V(t) = V_0(1 - r)^t$$
where $V_0 = 15500$ (initial value), $r = 0.05$ (depreciation rate), $t$ = number of years.

Step2: Calculate time elapsed

$t = 2005 - 2001 = 4$ years

Step3: Plug values into formula

$$V(4) = 15500(1 - 0.05)^4 = 15500(0.95)^4$$

Step4: Compute $(0.95)^4$

$0.95^4 = 0.95 \times 0.95 \times 0.95 \times 0.95 = 0.81450625$

Step5: Calculate final value

$$V(4) = 15500 \times 0.81450625 = 12624.846875$$

Step6: Round to nearest hundred

$12624.846875$ rounds to $12600$

Answer:

$\$12600$