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 will follow these steps:

### Step 1: Set up the differential equation
Given that the rate of growth of bacteria is proportional to the number present, we can express this mathematically as:
\[ \frac{db}{dt} = k \cdot b \]
where \( b \) is the number of bacteria and \( k \) is the proportionality constant.
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