Answer:
After 24 hours, there will be 4191 bacteria present in the culture.
Step-by-step explanation:
Initial number of bacteria = 300
amount in 10 hrs = 3 x 300 = 900
time taken = 10 hours
Bacterial growth is exponential, ans so we use the equation
N = N'[tex]e^{kt}[/tex]
where N is the final amount
N' is the initial amount
k is the growth constant
t is the time
For this first case, we have
900 = 300 x [tex]e^{k*10}[/tex]
3 = [tex]e^{10k}[/tex]
take natural log of both sides, we'll have
ln 3 = ln [tex]e^{10k}[/tex]
1.0986 = 10k
k = 1.0986/10 = 0.10986
using the growth constant above, we calculate for a day which is 24 hours
N = N'[tex]e^{kt}[/tex]
N = 300 x [tex]e^{0.10986*24}[/tex]
N = 300 x [tex]e^{2.637}[/tex]
N = 300 x 13.97
N = 4191 bacteria
