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

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An exponential growth function is typically of the form $$ f(x) = a \cdot b^x $$ where:
- $$ a $$ is a non-zero constant,
- $$ b > 1 $$ (which ensures growth as $$ x $$ increases).

Let's analyze each function:

1. **$$ f(x) = 6(0.25)^x $$**
   - **Base:** 0.25
   - Since $$ 0.25 < 1 $$, this is an exponential **decay** function, not growth.

2. **$$ f(x) = 0.25(5.25)^x $$**
   - **Base:** 5.25
   - Since $$ 5.25 > 1 $$, this is an exponential **growth** function.

3. **$$ f(x) = -4.25^x $$**
   - **Base:** 4.25
   - While $$ 4.25 > 1 $$ suggests growth, the negative sign means the function oscillates between positive and negative values for integer $$ x $$. Typically, exponential growth functions have positive coefficients, so this is **not** a standard exponential growth function.

4. **$$ f(x) = (-1.25)^x $$**
   - **Base:** -1.25
   - A negative base can lead to oscillating behavior depending on whether $$ x $$ is an integer. This does not represent a standard exponential growth function.

**Conclusion:** The only exponential growth function among the given options is:

$$ f(x) = 0.25(5.25)^x $$

**Answer:** Only the second function, f (x ) = 0.25 · (5.25)^x, is an exponential growth function.
The exponential growth function is $$ f(x) = 0.25(5.25)^x $$.

Which is an exponential growth function?

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