18 The exponentiat model below represents the balance of a loan, in dollars, $$ x $$ years from now. What is meaning of 1.07 in the model? $$ f(x)=17198(1.07)^{x} $$

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In the exponential model for the loan balance:

$$ f(x) = 17,\!198 \times (1.07)^x $$

- **$$ f(x) $$** represents the balance of the loan in dollars after $$ x $$ years.
- **$$ 17,\!198 $$** is the initial loan amount.
- **$$ 1.07 $$** is the **annual growth factor**.

### Meaning of 1.07:

- **Interest Rate Interpretation**: The number **1.07** breaks down into **1** (the original principal) plus **0.07** (a 7% interest rate). This means that each year, the loan balance increases by **7%**.
  
- **Growth Factor**: Specifically, **1.07** serves as the **multiplicative factor** by which the loan balance grows each year. So, every year, the current balance is multiplied by **1.07** to account for the interest accrued.

### Example:

After 1 year ($$ x = 1 $$):
$$ f(1) = 17,\!198 \times 1.07 \approx 18,\!302.86 $$

This shows that the loan balance increases by 7% after one year.

### Summary:

**1.07** in the model represents the **7% annual interest rate**, indicating that the loan balance grows by 7% each year.
In the loan balance model $$ f(x) = 17,\!198 \times (1.07)^x $$, the **1.07** represents a **7% annual interest rate**. This means the loan balance increases by 7% each year.

18 The exponentiat model below represents the balance of a loan, in dollars, \( x \) years from now. What is meaning of 1.07 in the model? \( f(x)=17198(1.07)^{x} \)

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