Question 1083545: A population of bacteria originates with 8,700 bacteria. After a harmful substance is introduced into the environment, the rate of decline of the bacteria population is 9% per hour. In addition, 50 bacteria are added to the population each hour. How many bacteria are in the population after three hours (round your answer to the nearest whole number)?
A) 7,300
B) 6,141
C) 6,693
D) 7,068
Answer by jim_thompson5910(35256)   (Show Source):
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Answer: Choice C) 6,693
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Explanation:
During the first hour, the population declines by 9%
New population = (old population) - (9% of old population)
New population = (8700) - (9% of 8700)
New population = (8700) - (0.09*8700)
New population = 8700 - 783
New population = 7917
After the 9% decline, we go from 8700 bacteria to 7917 bacteria.
But we add in an additional 50 new members:
New population = (old population) + 50
New population = 7917 + 50
New population = 7967
At the end of the first hour, the population is 7967.
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During the second hour, the population declines by 9%
New population = (old population) - (9% of old population)
New population = (7967) - (9% of 7967)
New population = (7967) - (0.09*7967)
New population = 7967 - 717.03
New population = 7249.97
New population = 7250 ... rounding to the nearest whole number
After the 9% decline, we go from 7967 bacteria to 7250 bacteria.
But we add in an additional 50 new members:
New population = (old population) + 50
New population = 7250 + 50
New population = 7300
At the end of the second hour, the population is 7300.
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During the third hour, the population declines by 9%
New population = (old population) - (9% of old population)
New population = (7300) - (9% of 7300)
New population = (7300) - (0.09*7300)
New population = 7300 - 657
New population = 6643
After the 9% decline, we go from 7300 bacteria to 6643 bacteria.
But we add in an additional 50 new members:
New population = (old population) + 50
New population = 6643 + 50
New population = 6693
At the end of the third hour, the population is 6693.
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We are done because the third hour is over.
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