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INDIGO
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AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 10.0 grams 11 Sep 2005, 22:53
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AMOUNT OF BACTERIA PRESENT
Time Amount
1:00 P.M. 10.0 grams
4:00 P.M. x grams
7:00 P.M. 14.4 grams

Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?
A. 12.0
B. 12.1
C. 12.2
D. 12.3
E. 12.4

Can someone pls explain why A is the answer?
Thanks



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AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 10.0 grams 12 Sep 2005, 00:02
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INDIGO
AMOUNT OF BACTERIA PRESENT
Time Amount
1:00 P.M. 10.0 grams
4:00 P.M. x grams
7:00 P.M. 14.4 grams

Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?
A. 12.0
B. 12.1
C. 12.2
D. 12.3
E. 12.4

Can someone pls explain why A is the answer?
Thanks
Show more


The question stem is that the bacteria increase is the same fraction during each of the 3-hour.

Let's take 12
So the increase in first period is 12-10/10=2/10 or 1/5 or 20%

For second period the fraction should be same that is 1/5 of 12 become 2.4

Adding up 12+2.4 is 14.4

Answer is A
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richardj
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AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 10.0 grams 12 Sep 2005, 04:02
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You can do it in one calculation using the geometric mean formula.

= sqrt (10.0 x 14.4) = sqrt (144) = 12.0
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vikramm
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AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 10.0 grams 12 Sep 2005, 07:26
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Its a simple ratio problem - fraction increase from 10 to x is the same as fraction increase from x to 14.4 or like richardj mentions... geometric mean.
10/x = x/14.4 => x^2 = 10*14.4=144 => x = 12

Kind of redundant but just to point.. treat this (and I mean this specific problem) like a ratio problem.
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INDIGO
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AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 10.0 grams 12 Sep 2005, 10:48
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Thank you guys,

I understand the ratio concept but would like to know more about the geometric mean formula.

What is the Geometric mean formula? Where else can we use it?

Thanks



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Hi there,
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Thank you for understanding, and happy exploring!