Nonlinear functions SAT question

Choice B is correct. Functions $f$ and $g$ are both exponential functions with a base of $0.40$. Since $0.40$ is less than $1$, functions $f$ and $g$ are both decreasing exponential functions. This means that $f(x)$ and $g(x)$ decrease as $x$ increases. Since $f(x)$ and $g(x)$ decrease as $x$ increases, the maximum value of each function occurs at the least value of $x$ for which the function is defined. It's given that functions $f$ and $g$ are defined for $x\ge 0$. Therefore, the maximum value of each function occurs at $x=0$. Substituting $0$ for $x$ in the equation defining $f$ yields $f(0)=33{(0.4)}^{0+3}$, which is equivalent to $f(0)=33{(0.4)}^3$, or $f(0)=2.112$. Therefore, the maximum value of $f$ is $2.112$. Since the equation $f(x)=33{(0.4)}^{x+3}$ doesn't display the value $2.112$, the equation defining $f$ doesn't display the maximum value of $f$. Substituting $0$ for $x$ in the equation defining $g$ yields $g(0)=33(0.16){(0.4)}^{0-2}$, which can be rewritten as $g(0)=33(0.16)(\frac{1}{{0.4}^2})$, or $g(0)=33(0.16)(\frac{1}{0.16})$, which is equivalent to $g(0)=33$. Therefore, the maximum value of $g$ is $33$. Since the equation $g(x)=33(0.16){(0.4)}^{x-2}$ displays the value $33$, the equation defining $g$ displays the maximum value of $g$. Thus, only equation II displays, as a constant or coefficient, the maximum value of the function it defines.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.