Kiran has a collection of vintage action figures that is worth $320. If the collection appreciates at a rate of 14.8% per year, which equation represents the value of the collection after 8 years? V=320(1+0.148) V=320(1.148)^(8) V=320(0.148)^(8) V=320(1-0.148)^(8)

Question

Kiran has a collection of vintage action figures that is worth  $320. If the collection appreciates at a rate of  14.8% per year, which equation represents the value of the collection after 8 years?  V=320(1+0.148)  V=320(1.148)^(8)  V=320(0.148)^(8)  V=320(1-0.148)^(8)

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Understand the problem: Understand the problem. We need to find the equation that represents the value of the collection after 8 years, given that it appreciates at a rate of 14.8% per year. The initial value of the collection is $320.Identify the correct formula: Identify the correct formula for appreciation. The formula for appreciation is the initial value multiplied by one plus the appreciation rate, raised to the power of the number of years. The general formula is V = P(1 + r)^t, where V is the final value, P is the initial value, r is the appreciation rate, and t is the time in years.Convert the percentage rate: Convert the percentage rate to a decimal. The appreciation rate is given as 14.8%, which as a decimal is 0.148.Apply the formula: Apply the formula to the given problem. Using the formula V = P(1 + r)^t, we substitute P = $320, r = 0.148, and t = 8 years to get the equation V = 320(1 + 0.148)^8.Check the answer choices: Check the answer choices to find the correct equation. The correct equation based on our calculation is V = 320(1.148)^8, which matches one of the given choices.

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