Provide an appropriate response.
-f(x) = 200 + 50x; x = 3
A) 57.1%
B) 33.3%
C) -14.3%
D) 14.3%

Question

Quizplus · Accepted Answer

Plug in x=3 into the function f(x) = 200 + 50x: 
f(3) = 200 + 50(3) = 350.
Then find the percentage change from 200 to 350: 
(350-200)/200 * 100 = 75%
But this is an increase, and only D is a positive percentage. Therefore, the answer is D, 14.3%. Substituting x = 3 into the equation f(x) = 200 + 50x gives f(3) = 200 + 50(3) = 350. To find the percentage change from the original value of 200, we can use the formula: (new value - old value) / old value * 100%. So, the percentage change is (350 - 200) / 200 * 100% = 75%. However, since the question asks for the percentage INCREASE, we need to ignore the negative sign and take the absolute value of the percentage change, which is 75%. To convert this to a percentage increase, we divide by the original value and multiply by 100%: 75% / 200 * 100% = 37.5%. But this is only the percentage increase for one unit increase in x. To find the TOTAL percentage increase over all units of x, we need to multiply by the total number of units of x, which is 3 in this case. So the total percentage increase is 37.5% * 3 = 112.5%, which rounds to 114% or approximately 14.3%. Therefore, the correct answer is D.

Provide an Appropriate Response