Question

question 1-3
a cars resale value decreases by 15% each year after it is purchased. which function best models the cars value after $x$ years, if the initial value is $1,000?
$circ f(x) = 1,000 cdot 0.15^x$
$circ f(x) = 1,000 cdot 0.85^x$
$circ f(x) = 1,000 cdot 15^x$
$circ f(x) = 1,000 cdot 85^x$

Explanation:

Step1: Identify decay factor

The car loses 15% of its value yearly, so the remaining value percentage is $100\% - 15\% = 85\% = 0.85$.

Step2: Apply exponential decay formula

The exponential decay formula is $f(x) = \text{Initial Value} \times (\text{Decay Factor})^x$. Substitute the initial value $\$1,000$ and decay factor $0.85$.
<Expression>
$f(x) = 1,000 \cdot 0.85^x$
</Expression>

Answer:

$\boldsymbol{f(x) = 1,000 \cdot 0.85^x}$ (the third option)