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The depreciation of the value of a recently purchased new car can be modeled by the equation:

$$f(x)=23,500(0.81)^{x}.$$

About how long will it take for its value to drop down to a value of $\$1000$?

$8\text{ years}$

$10\text{ years}$

$12\text{ years}$

$15\text{ years}$

$19\text{ years}$