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a bacteria population is growing exponentially so that it becomes six fold on 10 hours. at what time was it two fold?

User ThdK
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Answer:20.79

Explanation:

[ N = N₀ \cdot 2^{(t / 10)} ]

Where:

(N) is the final population (which is 6 times the initial population).

(t) is the time in hours.

Given that the final population is 6 times the initial population, we have:

[ N = 6N₀ ]

Substitute this into the exponential growth equation:

[ 6N₀ = N₀ \cdot 2^{(t / 10)} ]

Solving for (t):

[ 6 = 2^{(t / 10)} ]

Taking the natural logarithm (ln) of both sides:

[ \ln(6) = \frac{t}{10} \cdot \ln(2) ]

Solving for (t):

[ t = 10 \cdot \frac{\ln(6)}{\ln(2)} ]

Now, let’s calculate the value of (t):

[ t \approx 20.79 \text{ hours} ]

Therefore, the bacteria population was two-fold approximately 20.79 hours ago from the present time.

User MitchellJ
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