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

To determine which of the given functions represents **exponential growth**, let's analyze each one individually. An **exponential growth function** has the general form: \[ f(x) = a \cdot b^x \] where: - \( a \) is a constant, - \( b \) is the base of the exponential function, and - **For growth**, \( b > 1 \). Now, let's examine each function: 1. **\( f(x) = 6(0.25)^x \)** - **Base (\( b \))**: 0.25 - Since \( 0.25 < 1 \), this function represents **exponential decay**, not growth. 2. **\( f(x) = 0.25(5.25)^x \)** - **Base (\( b \))**: 5.25 - Here, \( 5.25 > 1 \), which signifies **exponential growth**. 3. **\( f(x) = -4.25^{x} \)** - This can be interpreted as \( f(x) = - (4.25)^x \). - Although the base \( 4.25 > 1 \) suggests growth in magnitude, the negative sign causes the function to decrease (since \( -(4.25)^x \) becomes more negative as \( x \) increases). Therefore, it's **not** a standard exponential growth function. 4. **\( f(x) = (-1.25)^x \)** - **Base (\( b \))**: -1.25 - A negative base introduces oscillations (positive and negative values) depending on whether \( x \) is even or odd. This behavior doesn't align with the typical definition of **exponential growth**, which requires a positive and growing trend. **Conclusion:** Among the provided options, only the second function exhibits the characteristics of an exponential growth function. **Answer:** Only the function \( f(x) = 0.25 \cdot (5.25)^{\,x} \) is an exponential growth function.