To determine the horizontal asymptote of the function \( y = 5(0.3)^x - 7 \), we need to analyze the behavior of the function as \( x \) approaches infinity.
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Exponential Decay Function: The term \( (0.3)^x \) represents an exponential decay function because the base \( 0.3 \) is between 0 and 1. As \( x \) increases, \( (0.3)^x \) approaches 0.
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Finding the Asymptote: As \( x \) approaches infinity, \( (0.3)^x \) will approach 0, thus:
\[ y \approx 5(0) - 7 = -7 \]
Therefore, the horizontal asymptote of the graph of this function is where the function approaches as \( x \) grows larger.
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Conclusion: The horizontal asymptote is at \( y = -7 \).
Response: The horizontal asymptote is at \( y = -7 \).
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