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A biotechnology student is performing an experiment in which he is trying to count the population of a bacteria after every hour. Each bacteria multiplies and becomes 8 times itself in 1 hour. But some of the bacteria die after every 2 hours. The population after 10 hours from the start of the experiment is what percentage of the initial population?
(1) The number of bacteria at the start of the experiment was 1 million.
(2) After every 2hours, 1/4th of the bacteria dies
(1) The number of bacteria at the start of the experiment was 1 million.
(2) After every 2hours, 1/4th of the bacteria dies
03 Jan 2022, 07:31
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Bunuel
A biotechnology student is performing an experiment in which he is trying to count the population of a bacteria after every hour. Each bacteria multiplies and becomes 8 times itself in 1 hour. But some of the bacteria die after every 2 hours. The population after 10 hours from the start of the experiment is what percentage of the initial population?
(1) The number of bacteria at the start of the experiment was 1 million.
(2) After every 2hours, 1/4th of the bacteria dies
(1) The number of bacteria at the start of the experiment was 1 million.
(2) After every 2hours, 1/4th of the bacteria dies
Rate of multiplication = 8times.
So if the number of bacteria in the start is x then after 1 hour it will become 8x after two hours it will become 64x.
some of the bacteria die after every 2 hours. |But we don't know how much or what percentage of the bacteria dies after two hours.
We need to find the % change in bacteria population after 10 hours.
If we can find out the rate of death we can find the % change. How.?
As the population after 10 hours will be in the form of x and which will cancel out when finding the % change.
(1) The number of bacteria at the start of the experiment was 1 million.
It tells us nothing about the death rate.
Not Sufficient.
(2) After every 2hours, 1/4th of the bacteria dies
Exactly what we were looking for.
Sufficient.
B is the answer.
28 Feb 2022, 00:46
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Bunuel
A biotechnology student is performing an experiment in which he is trying to count the population of a bacteria after every hour. Each bacteria multiplies and becomes 8 times itself in 1 hour. But some of the bacteria die after every 2 hours. The population after 10 hours from the start of the experiment is what percentage of the initial population?
(1) The number of bacteria at the start of the experiment was 1 million.
(2) After every 2hours, 1/4th of the bacteria dies
(1) The number of bacteria at the start of the experiment was 1 million.
(2) After every 2hours, 1/4th of the bacteria dies
Let the number of bacteria at the start of the experiment be x
After 1 hour
no. of bacteria= 8x
After 10 hours
no. of bacteria= \(8^{10}x\)- y ; where y is the number of bacteria that die after every 2 hours
Stmt 1
The number of bacteria at the start of the experiment was 1 million.
The value of y is still unknown. Insufficient.
Stmt 2
After every 2hours, 1/4th of the bacteria dies. This gives the value of y. Sufficient.
Since there is only one unknown variable, we can find what % of the initial population is the population after 10 hours.
Answer- B.
