Sure, let's break down the given function and fill in the blanks appropriately.
The function modeling the savings account balance is:
[tex]\[ f(x) = 500 \left(1 + \frac{0.015}{4}\right)^{4t} \][/tex]
1. The initial balance is represented by the coefficient before the parentheses. In this case, it is 500.
2. The compounding frequency is indicated by the number of compounding periods within a year. Since the 4 appears in the exponent, the account compounds quarterly.
3. The annual interest rate is represented by the number in the numerator inside the parentheses. Here, it is 0.015.
So, the initial balance is 500, the account compounds quarterly, and the interest rate is 0.015.
