The functions \( f \) and \( g \) are defined by the given equations, where \( x \geq 0 \). Which of the following equations displays, as a constant or coefficient, the maximum value of the function it defines, where \( x \geq 0 \) ? I. \( f(x)=18(1.25)^{x}+41 \) II. \( g(x)=9(0.73)^{x} \) A) I only B) II only C) I and II D) Neither I nor II

To find the maximum value defined by the functions \( f \) and \( g \) for \( x \geq 0 \), we analyze each function. For \( f(x) = 18(1.25)^{x} + 41 \), as \( x \) increases, \( (1.25)^{x} \) grows without bound, making \( f(x) \) increase indefinitely. However, the constant term \( 41 \) does represent a lower limit, but not a maximum. For \( g(x) = 9(0.73)^{x} \), since \( 0.73 < 1 \), as \( x \) increases, \( (0.73)^{x} \) approaches zero. Therefore, the maximum value of \( g(x) \) occurs at \( x=0 \), where \( g(0) = 9(0.73)^0 = 9 \). Thus, the equation displaying the maximum value for \( g(x) \) is 9, while \( f(x) \) has no maximum but a lower bound defined by the term 41. The answer is B) II only.