Dominic bought stock in a company two years ago that was worth x dollars. During the first year that he owned the stock, it increased by 31%. During the second year the value of the stock increased by 6%. Write an expression in terms of x that represents the value of the stock after the two years have passed.
Q. Dominic bought stock in a company two years ago that was worth x dollars. During the first year that he owned the stock, it increased by 31%. During the second year the value of the stock increased by 6%. Write an expression in terms of x that represents the value of the stock after the two years have passed.
Identify Initial Value and Increases: Identify the initial value of the stock and the percentage increases over the two years.Dominic's initial stock value: xx dollarsFirst year increase: 31%Second year increase: 6%We need to calculate the value of the stock after each year's increase.
Calculate First Year Value: Calculate the value of the stock after the first year's increase.To find the increased value, we multiply the initial value by 1 plus the percentage increase (expressed as a decimal).Value after first year = xx×(1+0.31)Simplify the expression.Value after first year = xx×1.31
Calculate Second Year Value: Calculate the value of the stock after the second year's increase.Now we take the value after the first year and increase it by 6%.Value after second year = (xx×1.31)×(1+0.06)Simplify the expression.Value after second year = (xx×1.31)×1.06
Combine Expressions for Total Value: Combine the expressions to represent the total value after two years.The final expression that represents the value of the stock after two years is:Final value = xx \times \(1.31) \times 1.06
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