Question

In a culture the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present?

• A. \( \frac{2}{\log 10} \log \left( \frac{11}{10} \right) \)
• B. \( 2 \log 2 \)
• C. \( \log 2 \log 11 \)
• D. \( \log 2 \log 11 \)

Hint:

The exponential growth model can be solved for time by equating the initial and final population in the growth formula.

Answer 1

The Correct Option is A

We know that the growth of the bacteria follows an exponential growth model. Using the formula for exponential growth \( N = N_0 e^{kt} \), where \( N_0 \) is the initial population and \( N \) is the population after time \( t \), we solve for the time it takes for the population to double. The correct formula results in \( \frac{2}{\log 10} \log \left( \frac{11}{10} \right) \).
Step 2: Conclusion.
The correct answer is (A).