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Re: The number of bacteria in a petri dish increased by 50 percent every 2 [#permalink]
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Hi All,

This question can be solved by TESTing THE ANSWERS and doing a bit of multiplication.

We're told that the number of bacteria in a petri dish increased by 50 PERCENT every 2 HOURS and that there were 108 million bacteria in the dish at 2:00 pm. We're asked at what time were there 32 million bacteria.

Since a 50% increase every 2 hours is HUGE, chances are that we're looking for a time sometime that 'morning'; answers A and B would be during the prior day's evening, which is so much further in the past that those answers are not logical.

Let's TEST Answer D: 8:00am

IF... there were 32 million bacteria at 8:00am....
there were 32 + (.5)(32) = 48 million bacteria at 10:00am...
there were 48 + (.5)(48) = 72 million bacteria at 12:00pm...
there were 72 + (.5)(72) = 108 million bacteria at 2:00pm...

This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer:

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Re: The number of bacteria in a petri dish increased by 50 percent every 2 [#permalink]
Bunuel wrote:
The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 00 p.m., at what time were there 32 million bacteria in the dish?

A. 6: 00 p.m.
B. 8: 00 p.m.
C. 6: 00 a.m.
D. 8: 00 a.m.
E. 10: 00 a.m.


We can think of this problem like finance problem

32(1 (1/2))^x= 108
3/2^x =108/32- simplify
3/2^x = 27/8

x= 3 -how many times increased- so if its done every 2 hours hours then it was done 6 hours ago which is 8:00 a.m

Thus
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The number of bacteria in a petri dish increased by 50 percent every 2 [#permalink]
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Bunuel wrote:
The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 00 p.m., at what time were there 32 million bacteria in the dish?

A. 6: 00 p.m.
B. 8: 00 p.m.
C. 6: 00 a.m.
D. 8: 00 a.m.
E. 10: 00 a.m.


\(32(1.5)^x=108\)

\((1.5)^x=\frac{108}{32}=\frac{27}{8}\)

\((\frac{15}{10})^x=\frac{27}{8}\)

\((\frac{3}{2})^x=\frac{27}{8}\)

\(x=3\)

\(\frac{27}{8}=\frac{27}{8}\)

50 percent increases in every 2 hours, So total hours \(= 3*2=6\)

The time when the bacteria were 32 million 2 pm-6 hours = 8 am
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The number of bacteria in a petri dish increased by 50 percent every 2 [#permalink]
Given: ]The number of bacteria in a petri dish increased by 50 percent every 2 hours.
Asked: If there were 108 million bacteria in the dish at 2: 00 p.m., at what time were there 32 million bacteria in the dish?

32*1.5ˆ(n/2) = 108
1.5ˆ(n/2) = 108/32 = 1.5ˆ3
n = 6

After n=6 hours, there were 108 million bacteria in the dish at 2: 00 p.m
At 8:00 am, there were 32 million bacteria in the dish.

IMO D
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The number of bacteria in a petri dish increased by 50 percent every 2 [#permalink]
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