The Correct Answer and Explanation is:
The correct answer is f(x) = q * 1.025^(x + 5).
Here is an explanation of how to arrive at this answer.
The problem gives us a starting function, f(x) = q * 1.025^x, which calculates the value of an investment. Let’s break down this function to understand its components. The variable q represents the initial amount of money, or principal, that was deposited into the account. The number 1.025 is the growth factor, indicating that the investment grows at an annual interest rate of 2.5% (since 1.025 is equivalent to 100% + 2.5%). The most important component for this question is the exponent, x, which represents the number of years the money has been in the account.
The question asks for a new equation that can determine the value of the account “5 years from now”. This means we need to account for five additional years of growth. If x is the number of years that have already passed, then five years into the future, the total amount of time the money will have been invested is the original x years plus the new 5 years. The new total time can be expressed as (x + 5).
To update the formula for this new time frame, we must substitute the original time variable x with our new expression for time, which is (x + 5). When we make this substitution in the exponent of the original function, we get the new equation: f(x) = q * 1.025^(x + 5).
This new function accurately calculates the account’s value at a point five years in the future from any given year x. The other options represent incorrect transformations. For example, using (x – 5) would calculate the value five years in the past, and multiplying x by 5 would represent a completely different growth scenario. Therefore, adding 5 to the exponent is the correct modification.
