Middle School:
Question: Bill's science fair project is to test the different bacteria in the mouths of dogs and people. He swabs his own mouth and his dog's mouth and then dabs a square centimeter of each in separate petri dishes. If the human mouth bacteria colony grows by a factor of 3 each day and the dog bacteria colony grows by a factor of 1.5 each day, then how much bigger will the area covered by the human bacteria be after 3 days?
Answer: 23.625 square centimeters
Solution: Over three days, the human bacteria colony triples in area 3 times. So, the human bacteria colony will be 1 × 3 × 3 × 3 = 27 square centimeters. The dog bacteria does the same thing, but its factor is 1, so it will be 1 × 1.5 × 1.5 × 1.5 = 3.375. So, the human bacteria colony is 27 – 3.375 = 23.625 square centimeters bigger.
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