Question

in the year 2010, a person bought a new car for $26000. for each consecutive year after that, the value of the car depreciated by 10%. how much would the car be worth in the year 2014, to the nearest hundred dollars?

Explanation:

Step1: Define depreciation formula

The value of the car after $n$ years follows the exponential depreciation formula:
$$V = V_0(1 - r)^n$$
where $V_0 = 26000$, $r = 0.10$, and $n$ is the number of years.

Step2: Calculate years of depreciation

From 2010 to 2014, $n = 2014 - 2010 = 4$ years.

Step3: Substitute values into formula

$$V = 26000(1 - 0.10)^4 = 26000(0.90)^4$$

Step4: Compute $(0.90)^4$

$$0.90^4 = 0.90 \times 0.90 \times 0.90 \times 0.90 = 0.6561$$

Step5: Calculate final value

$$V = 26000 \times 0.6561 = 17058.6$$

Step6: Round to nearest hundred

$17058.6$ rounded to the nearest hundred is $17100$.

Answer:

$\$17100$