Question

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

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

Answer 1

Step 1 :

The verbal statement is " The rate of change of with respect to is proportional to ".

Rate of change of with respect to : .

.

The differential equation for the verbal statement is , where is a constant.

Step 2 :

The differential equation is .

Integrate the above equation with respect to .

The solution of the differential equation is .

Solution :

The differential equation is .

The solution of the differential equation is .