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 rate

The car retains $1 - 0.15 = 0.85$ of its value yearly.

Step2: Apply exponential decay formula

The general form is $f(x) = \text{Initial Value} \times (\text{Retention Factor})^x$. Substitute values:
$f(x) = 1000 \times 0.85^x$

Answer:

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