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{:("Quantity A","Quantity B"),((0.99)^(y...

`{:("Quantity A","Quantity B"),((0.99)^(y),0.99xxy):}`

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The correct Answer is:
To compare the two quantities given in the question, we have: - Quantity A: \( (0.99)^y \) - Quantity B: \( 0.99 \times y \) We need to analyze the relationship between these two quantities for different values of \( y \). ### Step 1: Evaluate for \( y = 0 \) For \( y = 0 \): - Quantity A: \[ (0.99)^0 = 1 \] - Quantity B: \[ 0.99 \times 0 = 0 \] **Comparison**: \[ 1 > 0 \quad \Rightarrow \quad \text{Quantity A} > \text{Quantity B} \] **Hint**: Remember that any non-zero number raised to the power of 0 is 1, and any number multiplied by 0 is 0. ### Step 2: Evaluate for \( y = 1 \) For \( y = 1 \): - Quantity A: \[ (0.99)^1 = 0.99 \] - Quantity B: \[ 0.99 \times 1 = 0.99 \] **Comparison**: \[ 0.99 = 0.99 \quad \Rightarrow \quad \text{Quantity A} = \text{Quantity B} \] **Hint**: When \( y = 1 \), both quantities are equal, which shows that the relationship can change based on the value of \( y \). ### Step 3: Evaluate for \( y = 2 \) For \( y = 2 \): - Quantity A: \[ (0.99)^2 \approx 0.9801 \] - Quantity B: \[ 0.99 \times 2 = 1.98 \] **Comparison**: \[ 0.9801 < 1.98 \quad \Rightarrow \quad \text{Quantity A} < \text{Quantity B} \] **Hint**: As \( y \) increases, \( 0.99 \times y \) increases linearly, while \( (0.99)^y \) decreases exponentially. ### Conclusion From the evaluations: - For \( y = 0 \): Quantity A > Quantity B - For \( y = 1 \): Quantity A = Quantity B - For \( y = 2 \): Quantity A < Quantity B Since the relationship between Quantity A and Quantity B varies depending on the value of \( y \), we cannot determine a consistent relationship between the two quantities. Thus, the answer is: **Option D: The relationship cannot be determined from the information given.**
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