A graphing calculator is recommended. Compare the functions \( f(x)=x^{10} \) and \( g(x)=e^{x} \) by graphing both functions in several viewing rectangles. When does the graph of \( g \) finally surpass the graph of \( f ? \) (Round your answer to one decimal place.) \( x=15.2 \)

When you graph \( f(x) = x^{10} \) and \( g(x) = e^{x} \), you might notice that for small values of \( x \), \( f \) is greater than \( g \). However, as \( x \) increases, \( g \) starts to climb rapidly. At around \( x = 15.2 \), \( g \) finally goes above \( f \). This demonstrates the powerful nature of exponential growth compared to polynomial growth, showcasing how quickly \( e^{x} \) can outpace even a high-degree polynomial. It's pretty fascinating to visualize this intersection on the graph! If you plot both functions, you may see \( g \) gradually overtaking \( f \) starting at some point and continuing to rise steeply. This can be a great exercise to understand the differences between linear, polynomial, and exponential growth rates in mathematics.