A researcher places two colonies of bacteria into two petri dishes that each have area 10 square centimeters. After the initial placement of the bacteria the researcher measures and records the area covered by the bacteria in each dish every ten minutes. The data for each dish were fit by a smooth curve, as shown above, where each curve represents the area of a dish covered by bacteria as a function of time, in hours. Which of the following is a correct statement about the data above?
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At time both dishes are 100% covered by bacteria.
At time bacteria covers 10% of Dish 1 and 20% of Dish 2.
At time Dish 2 is covered with 50% more bacteria than Dish 1.
For the first hour, the area covered in Dish 2 is increasing at a higher average rate than the area covered in Dish 1.
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Choice B is the correct answer. Each petri dish has area 10 square centimeters, and so at time Dish 1 is 10% covered and Dish 2 is 20% covered Thus the statement in B is true.
Choice A is not the correct answer. At the end of the observations, both dishes are 100% covered with bacteria, but at time neither dish is 100% covered.
Choice C is not the correct answer. At time Dish 1 is covered with 50% less bacteria than is Dish 2, but Dish 2 is covered with 100% more, not 50% more, bacteria than is Dish 1.
Choice D is not the correct answer. After the first hour, it is still true that more of Dish 2 is covered by bacteria than is Dish 1, but for the first hour the area of Dish 1 that is covered has been increasing at a higher average rate (about 0.8 sq cm/hour) than the area of Dish 2 (about 0.1 sq cm/hour).
Students must synthesize graphical and textual information and determine what information is relevant to the solution.