Question

svlc algebra 1b - standard (15261)
exponential decay functions
modeling with exponential decay functions
jacob estimates that his car loses 12% of its value every year. the initial value is $12,000. which best describes the graph of the function that represents the value of the car after x years?
$f(x)=12,000(0.88)^x$ with a horizontal asymptote of $y=0$
$f(x)=12,000(0.12)^x$ with a horizontal asymptote of $y=0$
$f(x)=(12,000 - 0.88)^x$ with a vertical asymptote of $x=0$
$f(x)=12,000(1.12)^x$ with a vertical asymptote of $x=0$

Explanation:

Step1: Identify decay factor

The car loses 12% value yearly, so the remaining value percentage is $100\% - 12\% = 88\% = 0.88$. This is the decay factor.

Step2: Write decay function

The initial value $a=12000$, decay factor $b=0.88$. The exponential decay function is $f(x) = ab^x = 12000(0.88)^x$.

Step3: Determine asymptote

For exponential decay functions of the form $f(x)=ab^x$ where $0

Answer:

$f(x) = 12,000(0.88)^x$ with a horizontal asymptote of $y = 0$