At this moment, a bacteria colony has a volume of 9.3 cubic centimeters. The bacteria colony is growing continuously at a daily rate of 2.3%. At this rate, how long will it be before the bacteria colony outgrows the 46.5 cubic centimter container in which it is stored? Express your answer accurate to 1 decimal place.
_________ hours
2007-11-17 08:56:16 · 3 answers · asked by lauren m 1 in Science & Mathematics ➔ Mathematics
1728. One thousand seven hundred twenty eight hours.
Begin with 9.3 cubic centimeters and a growth rate of 2.3% which means 1.023 is your multiplier.
multiply 9.3 times 1.023 and that's how large it is after one day.
multiply THAT answer by...1.023, same growth rate, right...and THAT is the answer for the second day. Continue doing this until your volume is the first volume over 46.5 cubic centimeters. That occurs in 72 days. So, 72 days times 24 hours per day equals 1728 hours.
I don't want to break it down to decimals. You do that. It shouldn't be THAT hard...
And one more thing. The asked for the answer in HOURS, not days.
2007-11-17 09:12:39 · answer #1 · answered by Anonymous · 0⤊ 0⤋
You have to create an exponential equation of the form:
A = ab^t, where A is the ending amount, a is the initial amount, b is the rate of growth, and t is the time.
Make an exponential equation: V = 9.3(1.023)^t, where V is volume (ending amount) and t is time in hours, 1.023 is the rate of growth (since it GROWS by 2.3%, or 0.023, add this to 1), 9.3 is the initial amount.
Substitute 46.5 into V and solve using logarithms.
46.5 = 9.3(1.023)^t
5 = 1.023^t
log 5 = t log 1.023
t = (log 5)/(log 1.023) which is approx equal to 70.777 hrs.
This rounds to 70.8 hours.
Hope that helps!
2007-11-17 17:04:03 · answer #2 · answered by Anonymous · 0⤊ 0⤋
V= 9.3*(1.023)^t
You have to calculate t
ln(46.5/9.3) /ln(1.023) =t=70.8 daysrounded to 1 decimal place
If you want it exact to one decimal place the last figure should be 7
(t=70.7772 days)
2007-11-17 17:05:27 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋