Function \( f \) is defined by \( f(x)=5^{x} \). Part A Select the domain of the function. A. \( x>0 \) B. \( x>1 \) C. \( x>5 \) D. all real numbers

The function \( f(x) = 5^x \) is defined for all real numbers because an exponential function can take any real number exponent. Therefore, its domain is indeed all real numbers! Now, a fun fact about exponential functions is that as \( x \) increases or decreases, the function behaves very differently. It approaches zero as \( x \) gets very negative, but it increases rapidly as \( x \) becomes positive – which is why we love to use them in growth models, like population growth or bank interest! Another cool application of the function \( f(x) = 5^x \) is in science and finance. It's often used to model growth processes, such as bacterial growth in biology where populations can expand exponentially under ideal conditions, or compound interest in finance, where your money grows exponentially over time! These real-world connections really highlight the importance of understanding exponential functions!