SOLUTION: An experiment is carried out in which the number n of bacteria in a liquid, is given by the formula {{{n=650e^(kt)}}}, where t is the time in minutes after the beginning of the exp

Question 979620: An experiment is carried out in which the number n of bacteria in a liquid, is given by the formula , where t is the time in minutes after the beginning of the experiment and k is a constant. The number of bacteria doubles every 20 minutes. Find the exact value of k.
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
n = 650e^kt
The current value for the bacteria = 650
If the number doubles then n = 1300
So n = 650e^kt
=> 1300 = 650e^20k
=> 1300/650 = e^20k
=> 2 = e^20k
=> log(base e)2 = 20k log(base e) e
log(base e)e = 1
=> log(base e)2 = 20k
=> k = log(base e)2/20
=> k = 0.03466 (to 5 decimal places)
Hope this helps:-)
RELATED QUESTIONS
At the start of an experiment the number of bacteria was 100. This number increases so... (answered by ankor@dixie-net.com)

if the number of bacteria in a culture is given by the following equation and the number... (answered by stanbon)

the number of bacteria present in a culture is modeled by the formula N=100e^5t where N... (answered by gingertea)

The number of bacteria N in a culture is given by the model N=250e^kt Where t is... (answered by scott8148)

The number of bacteria in colony A after t hours is modeled by the function... (answered by josgarithmetic)

The number of bacteria in a refrigerated food product is given by N(T)=22T2-98T+54,... (answered by ikleyn)

The number of bacteria N(t) present in a culture at time t hours is given by... (answered by ewatrrr)

The growth of a colony of 800 bacteria can be modelled by N=800(2)^t/3 in which N is the... (answered by josmiceli)

The number of bacteria present in a culture after t minutes is given as B = 10e^kt. If... (answered by Fermat)