- 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?
Correct answer: C (parsed from the explanation — this source omits an answer key for this item)
Explanation
( )= ( )x Choice C is correct. For a function of the form f x a r 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.
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