OG详解-OG7 数学1 Q37

Choice B is correct. Each of the given choices is an equation of the form f(x) = a(b)^x-k , where a, b, and k are constants. For an equation of this form, the coefficient, a, is equal to the value of the function when the exponent is equal to   0, or when x = k. It follows that in the equation f(x) = 33(1.5)^x , the coefficient, 33, is equal to the value of f(0). Substituting 0 for x in this equation yields f(0) = 33(1.5)⁰ , which is equivalent to f(0) = 33(1), or f(0) = 33. Thus, the value of c is 33 and the equation f(x) = 33(1.5)^x  shows the value of c as the coefficient.
Choice A is incorrect. This equation shows the value of f(-1), not f(0), as the coefficient. Choice C is incorrect. This equation shows the value of f(1), not f(0),  as the coefficient. Choice D is incorrect. This equation shows the value of f(2), not f(0), as the coefficient.