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: .
Assuming there was no ice 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: .