OG详解-OG3 数学2 Q21

Choice D is correct.  Since the value of y increases by a constant factor,  4, for each increase of 1 in the value of x , the relationship between x  and  y is exponential. An exponential relationship between x and y can be represented by an equation of the form y = a (b)^x , where a is the value of x when y = 0  and y increases by a factor of  b for each increase of 1 in the value of x . Since y = 200 when x = 0, a = 200. Since y  increases by a factor of 4  for each increase of 1 in the value of x , b = 4. Substituting 200 for a and 4  or b in the equation y = a (b)^x  yields y = 200 (4)^x . Thus, the equation y = 200 (4)^x represents the relationship between  x and y.
Choice A is incorrect and may result from conceptual errors. Choice B is incorrect. This equation represents a relationship where for each increase of  1 in the value of x , the value of y increases by a factor of  200 , not 4, and when x = 0, y is equal to 4, not 200. Choice C is incorrect and may result from conceptual errors.