I thought i integrated it right using the power rule and adding C but I keep getting it wrong. Could you please point me in the right direction?

Question

Ice is forming on a pond at a rate given by dy/dt= k√t where y is the thickness of the ice in inches at time t measured in hours since the ice started forming, and k is a positive constant. Find y as a function of t. Assume there is no ice initially

I answered

2/3 kt^(3/2) +C but that was wrong. What did I do wrong?

Answer 1

dy/dt = kt^1/2

 

y(t) = kt^3/2 / (3/2) + c = (2/3)kt^3/2 + c

 

Your integral is correct.  Now apply the given initial condition to find c and complete the solution.

 

y(0) = 0 (no ice initially)

 

y(0) = (2/3)k(0)^3/2 + c = 0 + c = 0 ⇒ c = 0

 

Final answer:

 

y(t) = (2/3)kt^3/2