Hello, mathlete!

The rate, , at which ice is forming on a pond

is proportional to the square root of

Let be the thickness of the ice in inches at time

measured in hours since the ice started forming.

(a) Write the differential equation. Use as the proportionality constant.

We have: .(b) Solve the differential equation.

Separate variables: .

Integrate: .

Assuming there wasnoice at , we have: .

The ice-thickness function is: .

We are told: .when(c) If the thickness of the ice is 3 inches after 9 hours,

what is the value of ?

So we have: .

. . Therefore: .