The population of a country increases by 2% every year. If it increases `k` times in a century, then prove that `[k]=7,w h e r e[dot]` represents the greatest integer function.

Explanation

To solve the problem step by step, we will use the concept of compound interest to determine how much the population increases over a century with a 2% annual growth rate.

### Step 1: Understand the problem
The population of a country increases by 2% every year. We need to find how many times the population increases in 100 years and prove that the greatest integer function of that value is 7.

### Step 2: Use the compound interest formula
The formula for compound interest is given by:
\[
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