BACTERIAL GROWTH In biological research concerning population growth, an equation is used that is similar to the exponential equations encountered in the analysis of [latex]R C[/latex] circuits. Applied to a number of bacteria, this equation is [latex]N_{f}=N_{i} 2^{n}[/latex] where [latex]N_{f}[/latex] is the number of bacteria present after [latex]n[/latex] doubling times, [latex]N_{i}[/latex] is the number present initially, and [latex]n[/latex] is the number of growth cycles or doubling times. Doubling times vary according to the organism. The doubling time is about 30 days for the bacteria responsible for leprosy, and about 20 minutes for the Salmonella bacteria responsible for food poisoning. Suppose only 10 Salmonella bacteria find their way onto a turkey leg after your Thanksgiving meal. Four hours later you come back for a midnight snack. How many bacteria are present now?

The number of doubling times is [latex]240 \mathrm{~min} / 20 \min =12[/latex]. Thus, [latex]N_{f}=N i^{n}=(10 \text { bacteria })\left(2^{12}\right)=40 960 \text { bacteria }[/latex] So your system will have to deal with an invading host of about 41 000 bacteria, which are going to continue to double in a very promising environment.

Question 18.AP.5: BACTERIAL GROWTH In biological research concerning populatio...

College Physics

BACTERIAL GROWTH

In biological research concerning population growth, an equation is used that is similar to the exponential equations encountered in the analysis of $R C$ circuits. Applied to a number of bacteria, this equation is

$N_{f}=N_{i} 2^{n}$

where $N_{f}$ is the number of bacteria present after $n$ doubling times, $N_{i}$ is the number present initially, and $n$ is the number of growth cycles or doubling times. Doubling times vary according to the organism. The doubling time is about 30 days for the bacteria responsible for leprosy, and about 20 minutes for the Salmonella bacteria responsible for food poisoning. Suppose only 10 Salmonella bacteria find their way onto a turkey leg after your Thanksgiving meal. Four hours later you come back for a midnight snack. How many bacteria are present now?

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