Question

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
.

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 best 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.**

This statement correctly interprets the growth factor of \( 1.035 \), which indicates that the account's balance grows by 3.5% each year due to annual compound interest.

Here’s a brief explanation of the other options:
- A is incorrect because the initial balance is $1,000, not $1,035.
- B is misleading; the balance at the end of one year is actually \( s(1) = 1,000(1.035)^1 = 1,035 \), not $1,000.
- D is incorrect; the initial balance is not decreasing, and there's no indication of a 96.5% decrease. Rather, the growth in balance reflects an increase.