👉 Certainly! Consider a simple problem involving the calculation of compound interest, which involves exponential growth. Suppose you invest $1000 at an annual interest rate of 5%, compounded annually. The formula for compound interest is \( A = P(1 + r/n)^{nt} \), where \( A \) is the amount of money accumulated after \( n \) years, including interest; \( P \) is the principal amount (initial investment); \( r \) is the annual interest rate (decimal); \( n \) is the number of times interest is compounded per year; and \( t \) is the time in years. For our example, \( P = 1000 \), \( r = 0.05 \), \( n = 1 \) (compounded annually), and \( t = 10 \) years. Plugging these values into the formula gives \( A = 1000(1 + 0.05/1)^{1 \cdot 10} = 1000(1.05)^{10} \approx 1628.89 \). This means after 10 years, your investment will grow to approximately $1628.89, showcasing the power of exponential growth in finance.
