To determine the appropriate equation that represents the scenario where Ross has \[tex]$750 in a bank account that earns 9% annual interest, we need to classify the type of growth. In this case, the interest is compounded at a rate of 9% annually, indicating exponential growth.
### Step-by-Step Solution
1. Identify the Type of Growth:
- Since the interest is compounded annually, the growth is exponential, not linear.
2. Understand Exponential Growth Formula:
- The general formula for exponential growth is given by:
\[
f(x) = P \cdot (1 + r)^x
\]
where \( P \) is the principal amount (initial amount), \( r \) is the rate of growth, and \( x \) is the number of years.
3. Apply the Given Values:
- Initial amount (\( P \)) = \$[/tex]750
- Annual interest rate ([tex]\( r \)[/tex]) = 9% or 0.09
4. Construct the Exponential Growth Equation:
- Plugging in the values:
[tex]\[
f(x) = 750 \cdot (1 + 0.09)^x
\][/tex]
- Simplifying inside the parentheses:
[tex]\[
f(x) = 750 \cdot (1.09)^x
\][/tex]
5. Compare with Options:
- Linear: [tex]\( f(x) = 750 + 1.09x \)[/tex] – This option indicates linear growth, which isn't correct for compounded interest.
- Linear: [tex]\( f(x) = 750 + 0.09x \)[/tex] – This also represents linear growth and is incorrect.
- Exponential: [tex]\( f(x) = 750 \cdot (1.09)^x \)[/tex] – This correctly represents exponential growth with the correct rate and initial amount.
- Exponential: [tex]\( f(x) = 750 \cdot (0.09)^x \)[/tex] – This incorrectly uses the interest rate as the base, not reflecting the proper formula for exponential growth.
### Correct Answer:
The equation that best represents the scenario where Ross has \$750 in a bank account that earns 9% annual interest is:
[tex]\[
\text{Exponential: } f(x) = 750 \cdot (1.09)^x
\][/tex]
