SOLUTION: Bacteria were introduced to a petri dish. Two hours after the introduction, there were 120411 bacteria. After seven hours since the introduction, there were 1083699 bacteria. 1

Question 1004915: Bacteria were introduced to a petri dish. Two hours after the introduction, there were 120411 bacteria. After seven hours since the introduction, there were 1083699 bacteria.
1.) Find the growth rate of the bacteria. (round to 3 decimal places)
2.) How many bacteria were initially introduced to the Petri dish? (Round to the nearest bacteria).
3.) How many bacteria will there be after 12 hours? (Round to the nearest bacteria).
4.) How long does it take for the bacteria colony to reach 361233 bacteria? (round to 2 decimal places)

PLEASE HELP ME THIS IS REALLY IMPORTANT FOR ME TO UNDERSTAND, THANK YOU!!!!!

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
1) ln(N2/N1) = k(t2-t1)
where N1, N2 are bacteria counts at times t1 and t2, and k is the growth rate
ln(1083699 / 102411) = k(7-2)
2.359141339 = 5k
k = 0.471828268 approx 0.472
the growth rate k is 0.472 hour^-1
*****************************************************************************
2) t1 = 0
ln(102411/N1) = 0.472(2-0)
ln(102411/N1) = 0.944
use definition of natural log
102411/N1 = e^0.944
N1 = 102411 / e^0.944 = 39844.888514675
N1 = 39845 bacteria's
*****************************************************************************
3) ln(N2/39845) = 0.472(12-0)
ln(N2/39845) = 5.664
N2/39845 = e^5.664
N2 = 39845 * e^5.664 = 11487295.055974431
N2 = 11487295 bacteria's
*****************************************************************************
4) ln(361233/39845) = 0.472(t2-0)
2.204526253 = t2(0.472)
t2 = 4.670606467
t2 = 4.67 hours
*****************************************************************************

RELATED QUESTIONS
Bacteria were introduced to a petri dish. Two hours after the introduction, there were... (answered by josmiceli)

Bacteria were introduced to a petri dish. Two hours after the introduction, there were... (answered by ankor@dixie-net.com)

Bacteria were introduced to a petri dish. Two hours after the introduction, there were... (answered by rothauserc)

Bacteria were introduced to a petri dish. Two hours after the introduction, there were... (answered by josgarithmetic)

Hi, my daughter is in 7th grade PreAlgebra and we do not have our book yet. She has been (answered by Nate)

Bacteria X has a growth rate of 160 % per hour. Some amount of bacteria X are... (answered by ankor@dixie-net.com)

Suppose a particular antibiotic that is introduced to a petri dish containing 3000 newly... (answered by josgarithmetic)

In a bacteria strain, the number of bacteria doubles every 20 minutes. There were 8... (answered by ikleyn)

The number B of bacteria in a Petri dish culture after t hours is given by... (answered by nerdybill)