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 cars value? $f(x) = 20,000(0.15)^x$ $f(x) = 20,000(1.15)^x$ $f(x) = 20,000(1.85)^x$ $f(x) = 20,000(0.85)^x$

Explanation:

Step1: Recall depreciation formula

The general formula for exponential depreciation is \( f(x)=P(1 - r)^x \), where \( P \) is the initial value, \( r \) is the rate of depreciation (in decimal), and \( x \) is time.

Step2: Identify values

Here, \( P = 20000 \), \( r = 0.15 \) (15% as a decimal). So \( 1 - r = 1 - 0.15 = 0.85 \).

Step3: Substitute into formula

Substituting \( P = 20000 \) and \( 1 - r = 0.85 \) into the formula, we get \( f(x)=20000(0.85)^x \).

Answer:

\( f(x) = 20,000(0.85)^x \)