question 1-3\na cars resale value decreases by 15% each year after it is purchased. which function best…

question 1-3\na 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 $1,000?\n$circ f(x) = 1,000 cdot 0.15^x$\n$circ f(x) = 1,000 cdot 0.85^x$\n$circ f(x) = 1,000 cdot 15^x$\n$circ f(x) = 1,000 cdot 85^x$

question 1-3\na 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 $1,000?\n$circ f(x) = 1,000 cdot 0.15^x$\n$circ f(x) = 1,000 cdot 0.85^x$\n$circ f(x) = 1,000 cdot 15^x$\n$circ f(x) = 1,000 cdot 85^x$

Answer

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)