7
AssignmentMultiple Choice

Zero and Negative Exponents

Question 7 • JHS-Algebra 1A (full year)

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?

Answer
A
f(x) = 12,000(0.12)x, with a horizontal asymptote of y = 0
B
f(x) = 12,000(1.12)x, with a vertical asymptote of x = 0
C
f(x) = 12,000(0.88)x, with a horizontal asymptote of y = 0
D
f(x) = (12,000 0.88)x, with a vertical asymptote of x = 0

Explanation

A 12% yearly loss means the car keeps 100% − 12% = 88% of its value each year, so its value is multiplied by 0.88 annually. The function is f(x) = 12,000(0.88)^x. As x increases, the value approaches 0 without reaching it, so the graph has a horizontal asymptote at y = 0. Choice C matches both.

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