11
QuizMultiple Choice

Exponential Equations in Financial Contexts — Quiz

Question 11 • Advanced Financial Algebra

A car depreciates by an average of 12% annually. The purchase price of the car was $⁢65,223 To determine the number of years it will take the car to reach a value of $⁢39,113.93 , solve the equation 39 comma 113 point 9 3 is equal to 65 comma 223 times open paren 1 minus 0 point 1 2 close paren to the x th power Round to the nearest whole number if necessary.

Answer
A
13 years
B
12 years
C
3 years
D
4 years

Explanation

Divide the target value by the purchase price: 39,113.93 ÷ 65,223 ≈ 0.5997. The equation becomes 0.88^x ≈ 0.5997, since the car retains 88% of its value each year. Because 0.88^4 ≈ 0.5997, it will take about 4 years to reach that value. The correct choice is D, 4 years.

AI-written and checked against the verified answer.

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