A new car is purchased for 22300 dollars. The value of the car depreciates at 12.25% per year. To the nearest tenth of a year, how long will it be until the value of the car is 3700 dollars? Answer:

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A new car is purchased for 22300 dollars. The value of the car depreciates at  12.25% per year. To the nearest tenth of a year, how long will it be until the value of the car is 3700 dollars? Answer:

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Determine type of depreciation: Determine the type of depreciation. The car depreciates at a constant percentage each year. This is an example of exponential decay.Identify values: Identify the initial value (a), the rate of depreciation (r), and the final value (P(t)). Initial value, a = $22,300 Rate of depreciation, r = 12.25% or 0.1225 in decimal form Final value, P(t) = $3,700Set up 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 amount, and r is the rate of decay.Substitute values: Substitute the known values into the formula. $3,700 = $22,300 * (1 - 0.1225)^tSolve for t: Solve for t. First, divide both sides by $22,300 to isolate the exponential expression. (1 - 0.1225)^t = $3,700 / $22,300Calculate division: Calculate the division on the right side of the equation. (1 - 0.1225)^t = 0.1659192825Take natural logarithm: Take the natural logarithm of both sides to solve for t. ln((1 - 0.1225)^t) = ln(0.1659192825) t * ln(1 - 0.1225) = ln(0.1659192825)Calculate logarithms: Calculate the natural logarithms. t * ln(0.8775) = ln(0.1659192825) t * (-0.132289) = -1.797Solve for t: Solve for t by dividing both sides by ln(0.8775). t = -1.797 / -0.132289Calculate division: Calculate the division to find the value of t. t ≈ 13.584Round to nearest tenth: Round t to the nearest tenth of a year. t ≈ 13.6 years

A new car is purchased for $22300$ dollars. The value of the car depreciates at $12.25 \%$ per year. To the nearest tenth of a year, how long will it be until the value of the car is $3700$ dollars? $\newline$ Answer:

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A new car is purchased for 223002230022300 dollars. The value of the car depreciates at 12.25% 12.25 \% 12.25% per year. To the nearest tenth of a year, how long will it be until the value of the car is 370037003700 dollars?\newlineAnswer:

A new car is purchased for $22300$ dollars. The value of the car depreciates at $12.25 \%$ per year. To the nearest tenth of a year, how long will it be until the value of the car is $3700$ dollars? $\newline$ Answer: