The rate of change of the volume V with respect to time t of water leaking from a tank is proportional to the cube of the volume. Which of the following is a differential equation that could describe this relationship?

Step-by-step explanation:

Since:

V: volume

t: time

K: proporcional constant

dV/dt = K*V^3 ---> (V^-3)dV = Kdt

Integrating by parts:

Then:

If we call: K1 = -4K ; K2 = Vo^-4, (both constants) then:

If chose select the initial time into = 0, then:

The differential equation predicting the rate of change of volume will be where k is the constant.

Given information:

The rate of change of volume V with respect to time t of water leaking from a tank is proportional to the cube of the volume.

The volume is leaking from the tank. So, the rate can be written as negative.

According to the given condition, the rate of change of volume can be written as,

Here, k is the proportionality constant. Its value can be found by using the boundary conditions.

Therefore, the differential equation predicting the rate of change of volume will be where k is the constant.

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