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The number of bacteria P(h) in a certain population is given by the equation P(h) = 2100e^(0.13h). How many hours will it take for the number of bacteria to reach a certain value?

User Hatemjapo
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Final answer:

To find the number of hours it will take for the number of bacteria to reach a certain value, you can use the given equation P(h) = 2100e^(0.13h). By setting the equation equal to the desired value and solving for h, you can determine the number of hours.

Step-by-step explanation:

The given equation P(h) = 2100e^(0.13h) represents the number of bacteria in a population over time. In order to find the number of hours it will take for the number of bacteria to reach a certain value, we need to set the equation equal to the desired value and solve for h. Let's say the desired value is N: N = 2100e^(0.13h). To solve for h, we can take the natural logarithm of both sides: ln(N) = ln(2100e^(0.13h)). Using the properties of logarithms, we can simplify this to: ln(N) = ln(2100) + 0.13h. From here, we can isolate h by subtracting ln(2100) and dividing by 0.13: h = (ln(N) - ln(2100)) / 0.13.

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