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

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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:** $$ f(x)=0.25(5.25)^{x} $$
$$ f(x) = 0.25(5.25)^x $$ is an exponential growth function.

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

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