SOLUTION: The radius of a circle as a function of time is defined by the equation, r(t)=4t^2+3t+1. Determine the rate of change in the area of the circle when dr/dt=11.

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Question 596252: The radius of a circle as a function of time is defined by the equation, r(t)=4t^2+3t+1. Determine the rate of change in the area of the circle when dr/dt=11.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have

so when dr/dt = 11, t = 1.

The area of the circle as a function of time is





We differentiate both sides with respect to t:



Replace t = 1 to obtain

(units squared per unit of time)