Question

terrence buys a new car for $20,000. the value of the car depreciates by 15% each year. if $f(x)$ represents the value of the car after $x$ years, which function represents the car’s value? $f(x)=20,000(1.85)^x$ $f(x)=20,000(0.15)^x$ $f(x)=20,000(1.15)^x$

Explanation:

Step1: Identify depreciation rate

The car depreciates 15% yearly, so the remaining value percentage per year is $1 - 0.15 = 0.85$.

Step2: Apply exponential decay formula

The initial value $P_0 = 20000$, and the exponential decay function is $f(x) = P_0(1 - r)^x$, where $r$ is the depreciation rate. Substituting values gives $f(x) = 20000(0.85)^x$.

Step3: Match to options

The correct function corresponds to the (partially visible) last option, which is $f(x)=20,000(0.85)^x$.

Answer:

$f(x)=20,000(0.85)^x$ (the leftmost partially visible option)