Jasontuyj2012 wrote:

AMOUT OF BACTERIA PRESENT

Time Amount

1:00 pm 10.0 grams

4.00 pm x grams

7.00 pm 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 pm?

a) 12.0

b) 12.1

c) 12.2

d) 12.3

e) 12.4

Method I - Algebra - Multiplier

"The amount of bacteria present increased by the same fraction," \(x\), twice:

\((x*x) = x^2\) = the multiplier, twice

\(10 * x^2 = 14.4\)

\(x^2 = \frac{14.4}{10}\)

\(x = \sqrt{1.44}= 1.2 =\) the multiplier

Number of bacteria at 4 p.m.?

\(10 * 1.2 = 12\) bacteria present at 4 p.m.

(And \(12 * 1.2 = 14.4\) at 7 p.m. Correct.)

Answer A

Method II - Use answer choices

Start with (C) 12.2

Find one fractional increase:

\(\frac{12.2}{10} = 1.22\)

Result for the second fractional increase:

\(12 * 1.22 = 14.64\)

C's 4 p.m. value is too great. Eliminate D and E, which will be even greater.

Try A, the round number: 12

Fractional increase: \(\frac{12}{10} = 1.2\)

Multiply 4 p.m. value, 12, by 1.2:

\(12 * 1.2 = 14.4\). Correct.

Answer A