A principal of \( \$ 2000 \) was invested at \( 6.25 \% \) interest, compounded annually. Let \( t \) be the number of years since the start of the investment. Let \( y \) be the value of the investment, in dollars. Write an exponential function showing the relationship between \( y \) and \( t \).

The value of an investment compounded annually can be calculated using the formula \( y = P(1 + r)^t \), where \( P \) is the principal amount, \( r \) is the annual interest rate, and \( t \) is the number of years. In this case, \( P = 2000 \) and \( r = 0.0625 \). Thus, the exponential function representing the relationship between \( y \) and \( t \) is: \[ y = 2000(1 + 0.0625)^t \] This simplifies to: \[ y = 2000(1.0625)^t \] So, as time goes on, the value of your investment grows exponentially! Now, let's say you invested this money 10 years ago and want to know how much it would be worth today. Just plug in \( t = 10 \) into the exponential function, and you'll see how your money multiplies over the years thanks to the magic of compounding interest!