Which is an exponential growth function? \( f(x)=6(0.25)^{x} \) \( f(x)=0.25(5.25)^{x} \) \( f(x)=-4.25^{x} \) \( f(x)=(-1.25)^{x} \)

An exponential growth function has the form \( f(x) = a \cdot b^x \) where \( b > 1 \). This ensures that as \( x \) increases, \( f(x) \) grows exponentially. Let's analyze each function: 1. **\( f(x) = 6(0.25)^x \)** - Here, \( b = 0.25 \), which is less than 1. - This represents **exponential decay**, not growth. 2. **\( f(x) = 0.25(5.25)^x \)** - Here, \( b = 5.25 \), which is greater than 1. - This is an **exponential growth** function. 3. **\( f(x) = -4 \cdot 25^x \)** - Here, \( b = 25 \) (greater than 1) which indicates growth. - However, the negative coefficient (\( -4 \)) affects the direction but doesn't change the fact that the function is exponential. - While it represents exponential growth in magnitude, the negative sign might lead to confusion in some contexts. 4. **\( f(x) = (-1.25)^x \)** - The base \( -1.25 \) is negative. - Exponential functions typically require \( b > 0 \) to be well-defined for all real numbers \( x \). - This function is not standardly considered an exponential growth function. **Conclusion:** Among the given options, \( f(x) = 0.25(5.25)^x \) is the clear example of an exponential growth function. **Answer:** \( f(x)=0.25(5.25)^{x} \)