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M:C:MC:17

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PSAT 10

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Problem Solving and Data Analysis

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The figure presents a graph of two curves titled "Bacteria Growth." The horizontal axis is labeled "Time" in hours and the vertical axis is labeled "Area covered" in square centimeters. The numbers on each of the axes are from zero through 10, in increments of one.  The curve labeled "Dish 1" begins on the vertical axis at one and curves steeply up and to the right passing through the point with coordinates 2 comma 4, and the point with coordinates 3 comma 8.  The curve labeled "Dish 2" begins on the vertical axis at 2 and moves to the right before curving gradually up and to the right passing through the point with coordinates 3 comma 3, and the point with coordinates 5 comma 6.  The two curves intersect at the point that is a little more than one to the right of the vertical axis and a little more than 2 above the horizontal axis.

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 left parenthesis t space equals space 0 right parenthesis comma 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 t space equals space 0 comma both dishes are 100% covered by bacteria.

Correct Answer: 
No

At time t space equals space 0 comma bacteria covers 10% of Dish 1 and 20% of Dish 2.

Correct Answer: 
Yes

At time t space equals space 0 comma Dish 2 is covered with 50% more bacteria than Dish 1.

Correct Answer: 
No

For the first hour, the area covered in Dish 2 is increasing at a higher average rate than the area covered in Dish 1.

Correct Answer: 
No

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Choice B is the correct answer. Each petri dish has area 10 square centimeters, and so at time t space equals space 0 comma Dish 1 is 10% covered left parenthesis 1 over 10 right parenthesis and Dish 2 is 20% covered left parenthesis 2 over 10 right parenthesis. 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 t space equals space 0 comma neither dish is 100% covered.

Choice C is not the correct answer. At time t space equals space 0 comma 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).

Question Difficulty: 
medium
Objective: 

Students must synthesize graphical and textual information and determine what information is relevant to the solution.