To find the function \( f(x) \) that models the growth of the investment account, we start with the initial investment and the annual interest rate.
- The initial investment (\( a \)) is $3,500.
- The annual interest rate is 2.85%, which as a decimal is \( 0.0285 \).
- The growth factor \( b \) for the investment account would be \( 1 + \) interest rate. Therefore: \[ b = 1 + 0.0285 = 1.0285 \]
Now we can express the function in the form:
\[ f(x) = a \cdot b^x = 3500 \cdot (1.0285)^x \]
So the correct answer is:
\[ f(x) = 3,500 \cdot 1.0285^x \]
This is represented in your responses as:
f(x) = 3,500⋅1.0285^x.