The rate of growth of bacteria is proportional to the number present . If initially, there were 1000 bacteria and the number doubles in 1 hours. Find the number of bacteria after ` 2""1/2` hours . [ take ` sqrt 2 = 1.414]`

Explanation

To solve the problem of bacterial growth, we will follow these steps:

### Step 1: Set up the differential equation
The rate of growth of bacteria is proportional to the number present. We can express this as:
\[ \frac{dn}{dt} = k n \]
where \( n \) is the number of bacteria, \( t \) is time, and \( k \) is the proportionality constant.
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