A college fund is started with an initial deposit of \( \$ 2,000.00 \). The amount in the fu after \( x \) number of years is represented by the recursive equation \( f(x)=f(x-1) \cdot 1.06 \), in which \( f(0)=2,000 \). Use this recursive formula to create an exponential equation that models the fund's balance, \( A \), after \( t \) years, assuming there were no additional deposits or withdrawals. Which of the followir the correct equation? (1 point) \( A=2,000 e^{0.061 t} \) \( A=2,000 e^{0.058 t} \) \( A=2,000 e^{0.06 t} \) \( A=2,000 \cdot 1.06^{t} \)

To create an exponential equation from the recursive formula \( f(x) = f(x-1) \cdot 1.06 \) with \( f(0) = 2,000 \), we need to realize that this is a compound interest scenario where the balance grows by a factor of \( 1.06 \) each year. This leads to the exponential growth equation \( A = 2,000 \cdot 1.06^{t} \). When it comes to compound interest, understanding how money grows over time can be exciting! Each year, that interest not only gets applied to your initial amount but also compounds on the interest earned previously. This means that every dollar deposited is like a little employee that works hard to make more dollars! So, keep an eye on that balance; it'll multiply over time!