5
QuizMultiple Choice

Exponential and Logarithmic Functions — Test

Question 5 • Math 3

Devon purchased a new car valued at 16 dollars comma 000 that depreciated continuously at a rate of 35 percent Its current value is 2 dollars comma 000 The equation 2 comma 000 is equal to 16 comma 000 times open paren 1 minus r close paren to the t th power represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.

Answer
A
2 years
B
8 years
C
1 year
D
5 years

Explanation

Substitute the depreciation rate r = 0.35 into the equation: 2,000 = 16,000(0.65)^t. Dividing by 16,000 gives 0.125 = (0.65)^t, so t = ln(0.125) ÷ ln(0.65) ≈ 4.83. Rounded to the nearest whole number, Devon’s car is about 5 years old, choice D.

AI-written and checked against the verified answer.

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