OG详解-OG2 数学1 Q23

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 decreasingexponential 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.