Question

Ayushi plotted a graph determining her car's fuel economy as a function of speed. State the true among the following.

• A. The rate of increase in fuel economy below $50$ mph is greater than the rate of decrease in fuel economy above $50$ mph.
• B. The rate of increase in fuel economy below $50$ mph is equal to the rate of decrease in fuel economy above $50$ mph.
• C. Fuel economy peaks at $50$ mph, but nothing can be said about the rates of change in fuel economy above and below $50$ mph.
• D. The rate of increase in fuel economy below $50$ mph is less than the rate of decrease in fuel economy above $50$ mph.

Answer 1

The correct option is D The rate of increase in fuel economy below $50$ mph is less than the rate of decrease in fuel economy above $50$ mph.

The rate is calculated by calculating the slope.

Let us assume uniform rate, then before $50$ mph, $rate=\frac{41-27}{50}\left(approx\right)=0.28$.

After $50$ mph it is rate $=\frac{32-41}{80-50}=\frac{-9}{30}=-0.30\left(approx\right)$.

Hence, the rate of increase in less as compared to the rate of decrease.