Two variables, x and y , are related such that for each increase of 1 in the value of x

Question

Two variables, x and y , are related such that for each increase of 1 in the value of x , the value of y increases by a factor of 4 . When x = 0 , y = 200 . Which equation represents this relationship?

Accepted Answer

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 for 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.

Question 0fbeb1