Given that h=17 at time=0, how do I solve the differential equation dh/dt=-1/5h^1/2 for h as a function of t

Question

A coffeepot has the shape of a cylinder with radius 5 inches, as shown in the figure above. Let h be the depth of the coffee in the pot, measured in inches, where h is a function of time t, measured in seconds. The volume V of coffee in the pot is changing at the rate of -5πh^1/2.

Answer 1

Did you try to integrate dh/dt, and use the given initial condition to find the constant of integration? This approach should work.

 

h(t) = ∫(dh/dt)dt + C

 

You know dh/dt.

 

Find C using

 

h(0) = 17

 

Just do the integration and find C.