The rate of chane of V is proportional to V. when t = 0, V = 20, 000, and when t = 4, V = 12, 500.

Question

Write and solve the differential equation that models the verbal statement. Evaluate the solution at the specified value of the independent variable.

The rate of chane of V is proportional to V. when t = 0, V = 20, 000, and when t = 4, V = 12, 500. what is the value of v when t = 6?

Answer 1

Step 1 :

The rate of change of V  is proportional to V.

Where k  is proportionality constant.

Rewrite the above equation :

Apply integration on each side.

When .

Step 2 :

Substitute in equation (1).

When .

Substitute in equation (2).

Substitute in above equation.

When

Solution :

When