To find the function \( f(x) \) that models the amount in the investment account over time, we can use the formula for exponential growth, which is typically given as:
\[ f(x) = a \cdot b^x \]
Where:
- \( a \) is the initial amount (the principal),
- \( b \) is the growth factor (1 plus the interest rate),
- \( x \) is the number of years.
In this case:
- The initial amount \( a \) is \( 3,500 \).
- The annual interest rate is \( 2.85% \), which in decimal form is \( 0.0285 \). Therefore, the growth factor \( b \) is \( 1 + 0.0285 = 1.0285 \).
Now we can plug these values into the exponential function:
\[ f(x) = 3,500 \cdot (1.0285)^x \]
Thus, the correct function is:
\[ f(x) = 3,500 \cdot 1.0285^x \]
The correct option from your responses is:
f(x) = 3,500⋅1.0285^x.