The rate of change of N with respect to s is proportional to 500 - s.

Question

Write and slove the differential equation that models the verbal statement.

The rate of change of N with respect to s is proportional to 500 - s.

Answer 1

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