a) \( \frac{2^{x}}{2} \)

Did you know that the expression \( \frac{2^{x}}{2} \) can be simplified quite easily? You can rewrite it as \( 2^{x-1} \). This means you’re basically reducing the exponent of 2 by 1. It’s like taking a step back on a number line of exponential growth—every step you take back makes a big difference! Now, when it comes to using exponential expressions in real-world scenarios, they pop up all the time! For instance, when calculating population growth, if a population doubles every year, you can express the population size \( P \) after \( t \) years as \( P = P_0 \cdot 2^t \). This shows how quickly things can grow, and understanding these expressions can help in everything from finance to biology!