SOLUTION: A population of bacteria originates with 2,000 bacteria. After a harmful substance is introduced into the environment, the rate of decline of the bacteria population is 2% per hour

Question 1083546: A population of bacteria originates with 2,000 bacteria. After a harmful substance is introduced into the environment, the rate of decline of the bacteria population is 2% per hour. In addition, 35 bacteria are added to the population each hour. How many bacteria are in the population after two hours (round your answer to the nearest whole number)?
A) 1,995
B) 1,925
C) 1,852
D) 1,990
Found 2 solutions by Boreal, jim_thompson5910:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
After 1 hour, 2%, or 40 bacteria die and 1960 are left.
35 are added, so there are 1995, and 2% die off, or 39.90
That leaves 1955.10 or 1955 bacteria. Then 35 are added, and the population is 1990.10 or 1990.
D.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Answer: Choice D) 1,990

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Explanation:

During the first hour, the population declines by 2%
New population = (old population) - (2% of old population)
New population = (2000) - (2% of 2000)
New population = (2000) - (0.02*2000)
New population = 2000 - 40
New population = 1960

After one hour, we go from 2000 bacteria to 1960 bacteria.

But we add in an additional 35 new members:
New population = (old population) + 35
New population = 1960 + 35
New population = 1995

At the end of the first hour, the population is 1995.

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In the second hour, the population declines by another 2%
New population = (old population) - (2% of old population)
New population = (1995) - (2% of 1995)
New population = 1995 - 0.02*1995
New population = 1995 - 39.9
New population = 1955.1

So roughly 1955 individuals remain after the 2% decay

But we add in an additional 35 new members:
New population = (old population) + 35
New population = 1955 + 35
New population = 1990

We are done because the second hour is over.

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