A principal of \( \$ 3900 \) was invested at \( 6.75 \% \) interest, compounded annually. Let \( t \) be the number of years since the start of the imvestment. Let \( y \) be the value of the investmert im folli Write an exponential function showing the relationship betwoen \( y \) and \( t \).

The exponential function that represents the relationship between the value of the investment \( y \) and the number of years \( t \) can be expressed as: \[ y = 3900 \left(1 + \frac{6.75}{100}\right)^t \] or simplified to \[ y = 3900 (1.0675)^t. \] This equation captures how the principal amount grows over time, thanks to the magic of compound interest. If you’re curious about how this function relates to real-world investments, think of it this way: many savings accounts and investments work similarly. When you deposit money and allow it to compound, the interest earned in each period contributes to your total, leading to that exciting snowball effect called exponential growth! It's like a financial snowball rolling downhill, collecting more snow (interest) as it goes!