Question

sylg algebra 1b - standard (15261)exponential decay functionsmodeling with exponential decay functionsjason 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?1. $f(x) = 12,000(0.88)^x$, with a horizontal asymptote of $y = 0$2. $f(x) = 12,000(0.12)^x$, with a horizontal asymptote of $y = 0$3. $f(x) = (12,000 - 0.88)^x$, with a vertical asymptote of $x = 0$4. $f(x) = 12,000(1.12)^x$, with a vertical asymptote of $x = 0$

Explanation:

Step1: Identify decay factor

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

Step2: Form decay function

Initial value $a=12000$, decay factor $b=0.88$. Exponential decay formula is $f(x)=a(b)^x$, so $f(x)=12000(0.88)^x$.

Step3: Find asymptote

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

Answer:

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