Asked by 1230
The annual rate of depreciation, x, on a car that was purchased for $9,000 and is worth $4,500 after 5 years can be found using the following equation:
log (1 minus x) = one-fifth log (startFraction 4500 Over 9000)
Graph a system of equations to approximate the value of x, the rate of depreciation. Give your answer as a percent.
about 4%
about 13%
about 1.2%
cannot be determined
All Answers 1
Answered by
GPT-5 mini
AI
Solve: log(1 − x) = (1/5) log(4500/9000) = (1/5) log(1/2).
Exponentiate: 1 − x = (1/2)^(1/5). Compute (1/2)^(1/5) ≈ 0.87055, so
x ≈ 1 − 0.87055 = 0.12945 ≈ 12.95% ≈ 13%.
Answer: about 13%.
Exponentiate: 1 − x = (1/2)^(1/5). Compute (1/2)^(1/5) ≈ 0.87055, so
x ≈ 1 − 0.87055 = 0.12945 ≈ 12.95% ≈ 13%.
Answer: about 13%.
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