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OG 12 #80

by jimmynicho » Fri Jun 19, 2009 1:31 pm
Hi guys,

I didn't understamd the explanation in the book, any ideas?

Thanks

Amount of Bacteria
Time Amount
1:00pm 10.0 grams
4:00pm x grams
7:00pm 14.4 grams

Data for a certain biology experiment are given in the table above. If the amount of bacteria represent increased by the same factor during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:pm?

a) 12
b)12.1
c)12.2
d)12.3
e)12.4
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by vasbli » Fri Jun 19, 2009 1:42 pm
A.

increase by a factor means geometrical progression with factor a
Starting with 10

after 2 iterations, ie 7pm, population should reach 10axa=10a^2
hence 10a^2=14.4
a=1.2 or -1.2 but a>0, so i keep a=1.2 only

at 4pm, after 1 iteration of 3h, we have 10x1.2=12
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by ssmiles08 » Fri Jun 19, 2009 1:48 pm
Let k = constant.

we know the first number is 10.

to calculate x, 10 increases by a factor of k

x = 10*k

14.4 = x*k

substitute one equation into another.

10(k) = 14.4/(k)

(k)^2 = 1.44

square root both sides: k = 1.2

so to obtain x = 10(1.2) = 12

(A)
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