A new car is purchased for 20,000 dollars. The value of the car depreciates at a rate of 3.7% per year. Which equation represents the value of the car after 3 years? V=20,000(1-0.037) V=20,000(0.63)^(3) V=20,000(0.963)(0.963)(0.963) V=20,000(1.037)^(3)

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A new car is purchased for 20,000 dollars. The value of the car depreciates at a rate of  3.7% per year. Which equation represents the value of the car after 3 years?  V=20,000(1-0.037)  V=20,000(0.63)^(3)  V=20,000(0.963)(0.963)(0.963)  V=20,000(1.037)^(3)

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Identify values: Identify the initial value, depreciation rate, and time period. Initial value (P) = $20,000 Depreciation rate (r) = 3.7% per year Time (t) = 3 years We need to find the value of the car after 3 years, taking into account the annual depreciation rate.Convert to decimal: Convert the percentage depreciation rate to a decimal. To convert a percentage to a decimal, divide by 100. Depreciation rate (r) = 3.7% = 3.7/100 = 0.037Determine formula: Determine the formula for depreciation. The value of the car after a certain number of years can be calculated using the formula: V = P(1 - r)^t where V is the final value, P is the initial value, r is the depreciation rate, and t is the time in years.Substitute values: Substitute the values into the formula. Substitute P = $20,000, r = 0.037, and t = 3 into the formula. V = 20,000(1 - 0.037)^3Simplify expression: Simplify the expression inside the parentheses. 1 - 0.037 = 0.963 So the equation becomes: V = 20,000(0.963)^3Check options: Check the given options to see which one matches the simplified equation. The correct equation that represents the value of the car after 3 years is: V = 20,000(0.963)^3 This matches one of the given options.

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