Answer to Question #275741 in Algebra for aiden

Question

Jason 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(0.12)^x, with a horizontal asymptote of y = 0

f(x) = 12,000(1.12)^x, with a vertical asymptote of x = 0

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

f(x) = (12,000  0.88)^x, with a vertical asymptote of x = 0

Answer 1

$$f(x)=f(0)(1-r)^x$$

$$f(x)=12000(1-0.12)^x$$

$$f(x)=12000(0.88)^x$$

$$f(x)\to0\text{ as } x\to\infin$$

The horizontal asymptote is $y=0.$

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