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?\n$f(x)=20,000(0.85)^x$\n$f(x)=20,000(0.15)^x$\n$f(x)=20,000(1.15)^x$\n$f(x)=20,000(1.85)^x$

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?\n$f(x)=20,000(0.85)^x$\n$f(x)=20,000(0.15)^x$\n$f(x)=20,000(1.15)^x$\n$f(x)=20,000(1.85)^x$

Answer

Explanation:

Step1: Determine the depreciation factor

The car depreciates by 15% each year. So the remaining value of the car each year is 100% - 15%=85% or 0.85 in decimal form.

Step2: Write the exponential - decay function

The general form of an exponential - decay function is $f(x)=a(1 - r)^x$, where $a$ is the initial value, $r$ is the rate of decay, and $x$ is the number of years. Here, $a = 20000$ and $r=0.15$, so $f(x)=20000(0.85)^x$.

Answer:

$f(x)=20000(0.85)^x$ (the first option)