"A stone is dropped into a still pond. Concentric circular ripples spread out and the radius of the disturbed area increases at a rate of 16 cm/sec. At what rate does the area of the disturbed region increase when its radius is 4 cm?"
don't really know where to start.
I said A = πr^2 --> r = sqrt(A/π) --> d/dt(r) = sqrt(A/π) . d/dt
Now I'm lost...
dr/dt is notation. The r in that is not available to be multiplied.
Do not complicate things. You do exactly as I did, and just plug in. dr/dt is the rate at which the radius is changing. That was given in the problem, it is 16 cm/sec, so you just plug in dr/dt = 16 the form I gave you. Then, r = 4, and compute.