Answer :
Final answer:
The correct equation for the investment after t years with a 3.5% annual interest rate is A(t) = 7000(1.035)^t, illustrating the principle of compound interest.
Explanation:
The equation that best describes the investment after t years, given a principal amount of $7000 and an annual interest rate of 3.5%, is found using the formula for compound interest. You start your principal amount ($7000) and multiply it by 1 plus the annual interest rate (expressed as a decimal), raised to the power of the number of years t. Therefore, the correct equation is:
A(t) = 7000(1.035)^t
This is because each year, the account balances increases by a factor of 1 plus the interest rate. So if the rate is 3.5%, you would add 1 to 0.035 (the decimal form of 3.5%), giving you 1.035. Then, raise this to the power of t to account for the number of years the money is invested. This is how compound interest works to increase the value of the investment over time.
