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
OG 12 #80
This topic has expert replies
-
- Junior | Next Rank: 30 Posts
- Posts: 11
- Joined: Wed May 27, 2009 7:52 am
-
- Junior | Next Rank: 30 Posts
- Posts: 17
- Joined: Sat Mar 01, 2008 2:32 pm
- Location: Zurich
- Thanked: 1 times
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
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
- ssmiles08
- Master | Next Rank: 500 Posts
- Posts: 472
- Joined: Sun Mar 29, 2009 6:54 pm
- Thanked: 56 times
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)
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)