f x = 5,470 0.64 x 12 The function f gives the value, in dollars, of a certain piece of

Question

f x = 5,470 0.64 x 12 The function f gives the value, in dollars, of a certain piece of equipment after x months of use. If the value of the equipment decreases each year by p % of its value the preceding year, what is the value of p ?

Accepted Answer

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.

Question f-x-54