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?

Explanation

To solve the problem, we need to model the growth of bacteria using a differential equation. The growth rate of the bacteria is proportional to the number of bacteria present. Let's break down the solution step by step.

### Step 1: Set Up the Differential Equation
Given that the rate of growth of bacteria \( \frac{dB}{dt} \) is proportional to the number present \( B \), we can express this as:
\[ \frac{dB}{dt} = kB \]
where \( k \) is the proportionality constant.
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