MCAS 1999, 10th Grade Math, Questions 41-42

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Question #41 (Open-Response Question)

The number of bacteria in a sample doubles every four hours. At the end of 24 hours there are 30,720 bacteria present in a sample.

a. How many bacteria were present initially? Show your work.

b. During which four-hour period will 5 million bacteria first be present? Show your work.

c. Write a mathematical expression to determine the number of bacteria present at the end of any four-hour period.


Question #42 (Open-Response Question)

Mr. Daniels bought an above-ground cylindrical swimming pool that has a diameter of 20 feet.

He wants to find out how long it will take to fill his pool to a depth of 4 feet using his garden hose.

a. It takes him 15 seconds to fill a one-gallon jug. What is the rate of flow of the water from the hose in cubic inches per minute? (Note: 1 gal = 231 cubic inches)

b. Explain how to convert cubic inches to cubic feet.

c. If water is running at the same rate as in part a, how many hours will it take Mr. Daniels to fill his circular swimming pool to a depth of 4 feet? Explain or show how you found your answer.


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