Evaluate the solution at the specified value of the independent variable.

Question

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

The rate of change 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