Short Answer 
The total value of an account after a given period is represented by the equation f(x) = q ¬¨‚àë 1.025^x, where q is the initial deposit and 1.025 is the annual growth factor. To find the account’s value five years later, substitute x with x + 5, resulting in the equation f(x + 5) = q ¬¨‚àë 1.025^(x + 5), which reflects the compounded interest over the additional five years.
Step 1: Understand the Equation for Total Value
The function that describes the total value of the account is given by f(x) = q ¬¨‚àë 1.025^x, where q is the initial deposit and 1.025 reflects the account’s annual growth rate of 2.5%. This equation essentially shows how the value of the deposit grows over time due to interest accumulation. The variable x represents the number of years the money has been in the account.
Step 2: Substitute for 5 Years into the Equation
To find the total value of the account five years from now, we will replace x with x + 5 in the original equation. This adjustment allows us to calculate the account’s value after an additional five-year period without any further deposits or withdrawals. The updated equation will look like this: f(x + 5) = q ¬¨‚àë 1.025^(x + 5).
Step 3: Final Equation for 5 Years from Now
The resulting equation, after substitution, gives us the total value of the account five years later. It can be presented as f(x + 5) = q · 1.025^(x + 5). This representation indicates how the initial deposit q will grow when considering the compounded interest accumulated over the additional five years.