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In a certain population of microbes in a petri dish, the rate of

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In a certain population of microbes in a petri dish, the rate of  [#permalink]

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New post 01 Dec 2019, 03:40
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In a certain population of microbes in a petri dish, the rate of increase in the population is 9 percent per hour. The time it takes for a given population to double can be estimated using the formula \(70/t\) hours, where t is the rate of increase per hour expressed as a percent. If the number of microbes in the dish is 60,000 at the start of the first hour, what will be the approximate number of microbes after 48 hours?

A. 120,000
B. 420,000
C. 720,000
D. 1,900,000
E. 3,800,000
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In a certain population of microbes in a petri dish, the rate of  [#permalink]

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New post 01 Dec 2019, 10:33
No of hours to double the bacteria can be given as 70/9 = 7.7 hrs
in a cycle of 7.7 hrs, the population doubles
no of doubling cycles in 48 hours = 48/7.7 = 6.2.
Now no of microbes after 48 hrs = approx \(60000*2^6\)
hence approximate no of microbes 64*60000= 3800000

Hence the answer is 3800000 (E)

gmat1393 wrote:
In a certain population of microbes in a petri dish, the rate of increase in the population is 9 percent per hour. The time it takes for a given population to double can be estimated using the formula \(70/t\) hours, where t is the rate of increase per hour expressed as a percent. If the number of microbes in the dish is 60,000 at the start of the first hour, what will be the approximate number of microbes after 48 hours?

A. 120,000
B. 420,000
C. 720,000
D. 1,900,000
E. 3,800,000

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Re: In a certain population of microbes in a petri dish, the rate of  [#permalink]

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New post 01 Dec 2019, 17:59
how is 48 / 7.7 .. 5.something ? its 6.2 actually.. which makes it 2^6 doesn't it ?
gmatbusters let me what i'm doing wrong
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Re: In a certain population of microbes in a petri dish, the rate of  [#permalink]

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New post 01 Dec 2019, 18:18
You are right, that was a typo.

Amlu95 wrote:
how is 48 / 7.7 .. 5.something ? its 6.2 actually.. which makes it 2^6 doesn't it ?
gmatbusters let me what i'm doing wrong

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Re: In a certain population of microbes in a petri dish, the rate of   [#permalink] 01 Dec 2019, 18:18
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