Answer:5.48 days
Step-by-step explanation:
Given
Initial amount of bacteria [tex]x_o=20[/tex]
Final Population of bacteria [tex]x=2000[/tex]
[tex]r=0.825[/tex]
Using formula
[tex]x=x_o(2)^{\frac{T}{r}}[/tex]
where T=time in days
[tex]2000=20(2)^{\frac{T}{0.825}}[/tex]
[tex]100=2^{\frac{T}{0.825}}[/tex]
Taking log both side
[tex]\log_{10} (100)=\log _{10} (2^{\frac{T}{0.825}})[/tex]
[tex]2=\frac{T}{0.825}\log _{10}2[/tex]
[tex]T=\dfrac{2\times 0.825}{\log 2}[/tex]
[tex]T=5.48\ days[/tex]
