The radius of a circular oil spill after t minutes is given by r ( t ) = √ 16 t . Find the instantaneous rate at which the radius is growing after 30 minutes.

Question

Give your answer as a decimal approximation with at least 3 decimal places.

Answer 1

Answer 2

I'm going to assume that the equations for radius is r(t) = √(16t) and not (√16)(t)

To find the rate at which r changes with time, take the derivative with respect to time.

dr/dt = r'(t) = 1/2(16t)^-1/2(16) = 8(16t)^-1/2

r'(30) = 8(16•30)^-1/2 = 0.36515 (units/minute) [No length units are given so I just called it "units"]