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

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

Answer

Explanation:

Step1: Determine the decay factor

The car depreciates by 15% each year. The remaining value of the car each year is (100% - 15%=85% = 0.85).

Step2: Write the exponential - decay formula

The general formula for exponential decay is (f(x)=a(1 - r)^x), where (a) is the initial amount, (r) is the rate of decay, and (x) is the number of time - periods. Here, (a = 20000) (the initial value of the car), (r=0.15), and the function for the value of the car after (x) years is (f(x)=20000\times(1 - 0.15)^x=20000\times(0.85)^x).

Answer:

(f(x)=20000(0.85)^x) (corresponding to the first option in the multiple - choice list)