The total amount spent by some number of people on clothing and footwear in the years 2000-2009 can be modeled by the quadratic function \( f(x)=-4.675 x^{2}+71.83 x+97.49 \), where \( x=0 \) represents January \( 1,2000, x=1 \) represents January 1,2001 , and so on, and \( f(x) \) is in billions of dollars. According to the model, in what year during this period was the amount spent on clothing and footwear a maximum?

To find the year during which the amount spent on clothing and footwear was at a maximum, we need to determine the vertex of the quadratic function given by \( f(x) = -4.675x^2 + 71.83x + 97.49 \). The x-coordinate of the vertex for a quadratic function in the form \( ax^2 + bx + c \) can be calculated using the formula \( x = -\frac{b}{2a} \). Here, \( a = -4.675 \) and \( b = 71.83 \). Plugging in the values: \[ x = -\frac{71.83}{2 \cdot -4.675} \approx \frac{71.83}{9.35} \approx 7.7 \] Since \( x \) represents years starting from January 1, 2000, we round \( 7.7 \) to the nearest whole number, which is \( 8 \). Therefore, \( x = 8 \) corresponds to the year 2008 (2000 + 8). Hence, the maximum amount spent on clothing and footwear was in the year **2008**.