Posted by katrina on Tuesday, March 1, 2011 at 12:28am.
the amount of bacteria in a petri dish increased by a percent change of 12% each hour over a period of 15 hours.
a. find the growth factor for 1 hour?
b. by what total percent did the bacteria change during this 15 hour time period.?
c. how long will it take for the bacteria to double?

precalculus  drwls, Tuesday, March 1, 2011 at 9:16am
a. 1.12
b. [(1.12)^15 1] x 100
The x 100 is for conversion %
c. about 6 hours, using the "rule of 72"
For the exact answer (t), solve
(1.12)^t = 2

precalculas  Reiny, Tuesday, March 1, 2011 at 9:18am
your formula would be
Amount = a(1.12)^t , where 0 ≤ t ≤ 15
a) in 1 hour growth factor would be 1.12
b) Amount = a(1.12)^15 = 5.47a
percentage of growth = 5.47a/a = 5.47 or 547%
c)
2a = a(1.12)^t
2 = 1.12^t
log2 = log(1.12^t)
log2 = t log1.12
t = log2/log1.12 = 6.1

precalculas  drwls, Tuesday, March 1, 2011 at 9:25am
I do not agree with Reiny's answer #2. They asked for the change, so 1 must be subtracted from 1.12^15
This would result in a 447% increase, to 547% of the initial value

precalculas  Reiny, Tuesday, March 1, 2011 at 9:34am
drwls is correct, I should have subtracted to get the change.
(Can I blame it on the fact that I was only on my first cup of coffee ?)
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