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Data for a certain biology experiment are given in the table

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Re: Data for a certain biology experiment are given in the table [#permalink]

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New post 04 Apr 2018, 06:36
1
dave13 wrote:
AKProdigy87 wrote:
Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm:

Fractional increase from 1 PM to 4 PM = X / 10.0
Fractional increase from 4 PM to 7 PM = 14.4 / X

\(\frac{X}{10.0} = \frac{14.4}{X}\)

\(X^2 = (14.4)(10.0)\)

\(X^2 = 144\)

\(X = 12\)

Therefore, the correct answer is A: 12.0.


Hi pushpitkc

can you please explain why

here x is numerator Fractional increase from 1 PM to 4 PM = X / 10.0 ?

and here x is in denominator Fractional increase from 4 PM to 7 PM = 14.4 / X ?

many thanks!


Hey dave13

The answer to your question lies in the question stem
1:00 P.M. 10.0 grams
4:00 P.M. x grams
7:00 P.M. 14.4 grams

It is given that the bacteria increased by the same fraction during each of the two 3-hour periods

The increase in bacteria in the first three hour period = Bacteria(4 PM)/Bacterial(1 PM) = x/10
The increase in bacteria in the second three hour period = Bacteria(7 PM)/Bacterial(4 PM) = 14.4/x

Hope this helps you!
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Re: Data for a certain biology experiment are given in the table [#permalink]

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New post 06 Apr 2018, 08:45
tejal777 wrote:
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



We can let n = the multiplier for each 3-hour period. So, we have:

1 p.m. = 10 grams

4 p.m. = 10n

7 p.m. = 10n^2

We can create the following equation:

10n^2 = 14.4

n^2 = 1.44

n = 1.2

Thus, we have 10n = 10(1.2) = 12 grams of bacteria at 4 p.m.

Alternate Solution:

Since the fractional increase is the same for both 3-hour periods, we must have:

x/10 = 14.4/x

x^2 = 144

x = 12 or x = -12

Since the number of bacteria cannot be negative, the answer is 12.

Answer: A
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Re: Data for a certain biology experiment are given in the table   [#permalink] 06 Apr 2018, 08:45

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