terrence buys a new car for $20,000. the value of the car depreciates by 15% each year. if f(x) represents…

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 cars value?\no f(x)=20,000(0.85)^x\no f(x)=20,000(0.15)^x\no f(x)=20,000(1.15)^x\no f(x)=20,000(1.85)^x

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 cars value?\no f(x)=20,000(0.85)^x\no f(x)=20,000(0.15)^x\no f(x)=20,000(1.15)^x\no f(x)=20,000(1.85)^x

Answer

Explanation:

Step1: Understand depreciation formula

The formula for exponential - decay (depreciation) is $f(x)=a(1 - r)^x$, where $a$ is the initial amount, $r$ is the rate of decay as a decimal, and $x$ is the number of time - periods.

Step2: Identify values

The initial value of the car $a = 20000$, and the rate of depreciation $r=0.15$.

Step3: Substitute values into formula

Substitute $a = 20000$ and $r = 0.15$ into the formula $f(x)=a(1 - r)^x$. We get $f(x)=20000(1 - 0.15)^x=20000(0.85)^x$.

Answer:

$f(x)=20000(0.85)^x$