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

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

Answer

Explanation:

Step1: Understand depreciation formula

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

Step2: Identify values

Here, $P=$20000$, $r = 0.15$ (since 15% = 0.15), and $t=x$ (number of years).

Step3: Substitute values into formula

Substituting the values into the formula, we get $f(x)=20000(1 - 0.15)^x=20000(0.85)^x$.

Answer:

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