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Which of the following statements about the graph of 
y=12(0.75)^(x) is true?
Choose 1 answer:
(A) As 
x increases, 
y increases at an increasing rate.
(B) As 
x increases, 
y increases at a decreasing rate.
(C) As 
x increases, 
y decreases at an increasing rate.
(D) As 
x increases, 
y decreases at a decreasing rate.

Which of the following statements about the graph of y=12(0.75)x y=12(0.75)^{x} is true?\newlineChoose 11 answer:\newline(A) As x x increases, y y increases at an increasing rate.\newline(B) As x x increases, y y increases at a decreasing rate.\newline(C) As x x increases, y y decreases at an increasing rate.\newline(D) As x x increases, y y decreases at a decreasing rate.

Full solution

Q. Which of the following statements about the graph of y=12(0.75)x y=12(0.75)^{x} is true?\newlineChoose 11 answer:\newline(A) As x x increases, y y increases at an increasing rate.\newline(B) As x x increases, y y increases at a decreasing rate.\newline(C) As x x increases, y y decreases at an increasing rate.\newline(D) As x x increases, y y decreases at a decreasing rate.
  1. Analyze Function: We need to analyze the function y=12(0.75)xy=12(0.75)^{x} to determine how yy changes as xx increases. The base of the exponential function is 0.750.75, which is between 00 and 11.
  2. Identify Exponential Decay: Since the base 0.750.75 is less than 11, the function represents exponential decay. This means that as xx increases, the value of yy will decrease.
  3. Determine Rate of Change: Now we need to determine the rate of change of yy as xx increases. For an exponential decay function where the base is between 00 and 11, as xx increases, yy decreases at a decreasing rate. This is because each time xx increases by 11, yy is multiplied by the same factor of 0.750.75, which results in a smaller and smaller decrease in yy.
  4. Conclusion: Therefore, the correct statement about the graph of y=12(0.75)xy=12(0.75)^{x} is that as xx increases, yy decreases at a decreasing rate.

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