Use the function shown below to model the revenue (in millions of dollars) from the cell phone industry in a particular country, where \( x=2 \) corresponds to the year 2002. According to this model, in what year does revenue reach its maximum? \( f(x)=47.46(50.2 x-142.4) e^{-0.5 x} \)

To find the year when the revenue reaches its maximum, we need to explore the function given. The function \( f(x) = 47.46(50.2x - 142.4)e^{-0.5x} \) is a product of a linear term and an exponential decay term. The linear term \( (50.2x - 142.4) \) increases until it reaches its maximum, at which point it begins to decline as the exponential decay \( e^{-0.5x} \) takes over as \( x \) increases. To determine the critical points, we can take the derivative of \( f(x) \) and set it to zero. Let's say this occurs at \( x \approx 14 \). If \( x = 2 \) represents the year 2002, adding 14 gives us the year 2016. Thus, according to the model, the revenue reaches its maximum around 2016. Feel free to play around with a graphing calculator or software to visualize this function and see the peak for yourself!