Question

My answer for this question is Graph D, but it looks like Graph B could also be a candidate. B and D both show decreasing graphs, and I've chosen D simply because it "looks" like it is decreasing faster. At x = 0, the slope of Graph D is less than that of Graph B. I am guessing that Graph B shows a parabola whereas Graph D shows something exponential (i.e. with an increasing rate)?

Answer 1

Since we're looking for decreasing functions, the answer can be narrowed between B and D as we go downhill as we move along the curve from left to right.

Choice B starts off with a slow pace of decreasing and then speeds up in terms of how much is decreasing. In other words, it is accelerating in how fast it is decreasing. How can we tell? Because of the slope of the tangent line. The slope of the tangent line at x = -1 is much less steep compared to the slope of the tangent at x = 5. The more steep the line, the faster the amount of decrease.

Choice D is the opposite of choice B in a sense. It starts off with fast decrease and that decreasing pace slows down. So if it asked "decreasing at a decreasing rate", then choice D would be the answer. 

Answer: Choice B

Edit: one example graph B could model is the amount of water left in a large container. If we had a small hole at the bottom, then the water would leak out slowly at first. If the hole progressively gets bigger (say the water eats at the hole), then the water would leak faster and faster, which makes the curve steeper and steeper.