\ \

Step 1 :

The rate of change of N with respect s is proportional to $\"\"$ .

$\"\"$

Where k is proportionality constant..

Rewrite the above equation :

$\"\"$

Apply integration on each side.

$\"\"$

Consider $\"\"$ , then $\"\"$ .

Substitute $\"\"$ and $\"\"$ in equation (1). \ \

$\"\"$

Substitute $\"\"$ in above equation. \ \

$\"\"$ \ \

Solution :

The solution is $\"\"$