Ross has [tex]\$750[/tex] in a bank account that earns [tex]9\%[/tex] in annual interest. Select an equation that represents this scenario.

A. Linear: [tex]f(x) = 750 + 1.09x[/tex]
B. Linear: [tex]f(x) = 750 + 0.09x[/tex]
C. Exponential: [tex]f(x) = 750(1.09)^x[/tex]
D. Exponential: [tex]f(x) = 750(0.09)^x[/tex]



Answer :

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]