For the function q , the value of q x decreases by 45 % for every increase in the value

Question

For the function q , the value of q x decreases by 45 % for every increase in the value of x by 1 . If q 0 = 14 , which equation defines q ?

Accepted Answer

Choice C is correct. Since the value of q x decreases by a fixed percentage, 45 % , for every increase in the value of x by 1 , the function q is a decreasing exponential function. A decreasing exponential function can be written in the form q x = a 1 - p 100 x , where a is the value of q 0 and the value of q x decreases by p % for every increase in the value of x by 1 . If q 0 = 14 , then a = 14 . Since the value of q x decreases by 45 % for every increase in the value of x by 1 , p = 45 . Substituting 14 for a and 45 for p in the equation q x = a 1 - p 100 x yields q x = 14 1 - 45 100 x , which is equivalent to q x = 14 1 - 0.45 x , or q x = 14 0.55 x . 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. For this function, the value of q x increases, rather than decreases, by 45 % for every increase in the value of x by 1 .

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