Consider a savings account earning annual compound interest with no additional deposits or withdrawals made after the initial deposit. The balance in the account after x years can be modeled by the function s(x) = 1,000(1.035)x.

Question

Which statement is the best interpretation of one of the values in this function?
Responses
A The initial balance of this account is $1,035.The initial balance of this account is $1,035.
B The balance in the account at the end of one year is $1,000.The balance in the account at the end of one year is $1,000.
C The balance in the account increases at a rate of 3.5% each year.The balance in the account increases at a rate of 3.5% each year.
D The initial balance of the account decreases at a rate of 96.5% each year.

Answer 1

The correct interpretation of one of the values in the function \( s(x) = 1,000(1.035)^x \) is:

C. The balance in the account increases at a rate of 3.5% each year.

Explanation:

• The function models the balance in the account, where \( 1,000 \) is the initial deposit (the principal), and \( 1.035 \) represents the growth factor, which reflects an annual interest rate of 3.5% (since \( 1 + 0.035 = 1.035 \)).
• Therefore, the statement that the balance increases at a rate of 3.5% each year accurately describes the behavior of the function.

Let's briefly consider the other options:

• A: Incorrect, as the correct initial balance is $1,000, not $1,035.
• B: Incorrect, as the balance at the end of one year would be calculated as \( s(1) = 1,000(1.035)^1 = 1,035 \), not $1,000.
• D: Incorrect, as the initial balance does not decrease at any rate; it grows instead.