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A bacterial colony doubles in size every 30 minutes. If initially there are 40 bacteria present, the number of bacteria after t minutes can be modeled by the function N(t) = 40 - 2t/30How long does it take until there are 1,000 bacteria?

Answer :

[tex]N(t)=40\cdot2^{\frac{t}{30}}[/tex]

N=1000

we need to clear t of the model

[tex]1000=40\cdot2^{\frac{t}{30}}[/tex][tex]\frac{1000}{40}=2^{\frac{t}{30}}[/tex][tex]25=2^{\frac{t}{30}}[/tex][tex]\frac{t}{30}=\log _225[/tex]

[tex]\frac{t}{30}=\frac{\log 25}{\log 2}[/tex][tex]t=\frac{\log 25}{\log 2}(30)=139.31[/tex]

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