Quick Check Solutions Exponential Functions Target B
1) Since \( k(x) \) has an “\( a \)” value of \( 5 \), that means the y-intercept of the function is located at \( (0, 5) \). So \( k(x) \) would be vertically stretched in comparison to \( h(x) \).
2) To determine which function would grow more quickly you need to compare the “\( b \)” values, or growth factors, for each function. The “\( b \)” value of \( h(x) \) is \( 6 \) and the “\( b \)” value of \( k(x) \) is \( 4 \). Since the \( b \) value of \( h(x) \) is greater than \( k(x), h(x) \) would grow more quickly.
3) In order for the function to represent exponential decay, the “\( b \)” value must be between \( 0 \) and \( 1 \). In order for the function to be stretched, the “\( a \)” value would need to be greater than \( 1 \). One possible example would be \( y = 3 \cdot \left( \frac{1}{4} \right) ^x \)
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2) To determine which function would grow more quickly you need to compare the “\( b \)” values, or growth factors, for each function. The “\( b \)” value of \( h(x) \) is \( 6 \) and the “\( b \)” value of \( k(x) \) is \( 4 \). Since the \( b \) value of \( h(x) \) is greater than \( k(x), h(x) \) would grow more quickly.
3) In order for the function to represent exponential decay, the “\( b \)” value must be between \( 0 \) and \( 1 \). In order for the function to be stretched, the “\( a \)” value would need to be greater than \( 1 \). One possible example would be \( y = 3 \cdot \left( \frac{1}{4} \right) ^x \)
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