Select the best description of the following exponential equation. $$ f(x)=49(0.7)^{x} $$ Show your work here Hint: To add an exponent ( $$ x^{v} $$ ), type "exponent" or press "A" Gecaying by $$ 70 \% $$ with every unit of $$ x $$. Growing by $$ 30 \% $$ with every unit of $$ x $$. Decaying by $$ 30 \% $$ with every unit of $$ x $$.

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To determine the best description of the exponential equation $$ f(x) = 49(0.7)^x $$, let's analyze its components step-by-step.

### Understanding the Equation

The general form of an exponential function is:
$$ f(x) = a \cdot b^x $$
where:
- $$ a $$ is the initial value (when $$ x = 0 $$).
- $$ b $$ is the base that determines the growth or decay.
  - If $$ b > 1 $$, the function represents **growth**.
  - If $$ 0 < b < 1 $$, the function represents **decay**.

### Applying to $$ f(x) = 49(0.7)^x $$

1. **Initial Value ($$ a $$)**:
   - $$ a = 49 $$
   - This is the value of $$ f(x) $$ when $$ x = 0 $$.

2. **Base ($$ b $$)**:
   - $$ b = 0.7 $$
   - Since $$ 0.7 $$ is between 0 and 1, the function represents **decay**.

3. **Decay Rate**:
   - The base $$ 0.7 $$ can be interpreted as retaining 70% of the value with each unit increase in $$ x $$.
   - Therefore, the **decay rate** is $$ 30\% $$ (since $$ 100\% - 70\% = 30\% $$).

### Conclusion

The function $$ f(x) = 49(0.7)^x $$ **decays by 30% with every unit of $$ x $$**. This means that for each increase in $$ x $$, the value of $$ f(x) $$ decreases to 70% of its previous value, representing a 30% decay.

### Best Description

**Decaying by $$ 30\% $$ with every unit of $$ x $$.**
The function $$ f(x) = 49(0.7)^x $$ decays by 30% with every unit of $$ x $$.

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