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. \( \frac{2 \log 2}{\log 11} \)
• B. \( \frac{\log 2}{\log 11} \)
• C. \( \log 2 \)
• D. \( \frac{2 \log 2}{\log 11} \)

Hint:

Exponential growth can be solved using the equation \( N = N_0 e^{kt} \), and logarithms are useful for finding the rate constant.

Answer 1

The Correct Option is B

The bacteria count follows exponential growth, and the formula for exponential growth is \( N = N_0 e^{kt} \), where \( N_0 \) is the initial count, \( N \) is the final count, \( k \) is the rate constant, and \( t \) is time. After solving for the time, we find \( t = \frac{\log 2}{\log 11} \).