OG详解-OG4 数学2 Q23

Choice C is correct. For a function of the form  f(x )= a(r)x​k​  , where a, r , and k are constants and r <1, the value of f(x) decreases by 100(1-r)% for every increase of x by k. In the given function, a = 5,470, r = 0.64 , and k = 12. Therefore, for the given function, the value of f(x) decreases by 100(1-0.64)%, or 36%, for every increase of x by 12. Since f(x) represents the value, in dollars, of the equipment after x  months of use, it follows that the value of the equipment decreases every 12 months by  36%  of its value the preceding 12  months. Since there are 12 months in a year, the value of the equipment decreases each year by 36%  of its value the preceding year. Thus, the value of p is 36.
Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.