A new car is purchased for 18600 dollars. The value of the car depreciates at 14% per year. To the nearest tenth of a year, how long will it be until the value of the car is 6800 dollars? Answer:

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A new car is purchased for 18600 dollars. The value of the car depreciates at  14% per year. To the nearest tenth of a year, how long will it be until the value of the car is 6800 dollars? Answer:

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Identify type of depreciation: Determine the type of depreciation. The car depreciates at a constant percentage each year. This is an example of exponential decay.Find initial value, rate, final value: Identify the initial value (a), the rate of depreciation (r), and the final value (P(t)). Initial value (a) = $18,600 Rate of depreciation (r) = 14% per year or 0.14 as a decimal Final value (P(t)) = $6,800Set up exponential decay formula: Set up the exponential decay formula. The formula for exponential decay is P(t) = a * (1 - r)^t, where P(t) is the value after time t, a is the initial value, and r is the rate of decay.Plug in known values: Plug in the known values into the exponential decay formula. $6,800 = $18,600 * (1 - 0.14)^tSolve for t: Solve for t. First, divide both sides by $18,600 to isolate the exponential part of the equation. $6,800 / $18,600 = (1 - 0.14)^t 0.3655913978494624 = 0.86^tTake natural logarithm: Take the natural logarithm of both sides to solve for t. ln(0.3655913978494624) = ln(0.86^t)Use logarithm property: Use the property of logarithms that ln(a^b) = b * ln(a). ln(0.3655913978494624) = t * ln(0.86)Divide by ln(0.86): Divide both sides by ln(0.86) to solve for t. t = ln(0.3655913978494624) / ln(0.86)Calculate value of t: Calculate the value of t using a calculator. t ≈ ln(0.3655913978494624) / ln(0.86) t ≈ 7.267Round to nearest tenth: Round the answer to the nearest tenth of a year. t ≈ 7.3 years

A new car is purchased for $18600$ dollars. The value of the car depreciates at $14 \%$ per year. To the nearest tenth of a year, how long will it be until the value of the car is $6800$ dollars? $\newline$ Answer:

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A new car is purchased for $18600$ dollars. The value of the car depreciates at $14 \%$ per year. To the nearest tenth of a year, how long will it be until the value of the car is $6800$ dollars? $\newline$ Answer: