Let be the amount of lumber, in board-feet, produced from a tree of radius r (measured in inches). Which of the following gives the rate of change in the amount of lumber, in board-feet per inch, with respect to the radius when the radius is 21 inches?
C)r such that
D)r such that

Question

Let  be the amount of lumber, in board-feet, produced from a tree of radius r (measured in inches). Which of the following gives the rate of change in the amount of lumber, in board-feet per inch, with respect to the radius when the radius is 21 inches?
C)r such that 
D)r such that

Quizplus · Accepted Answer

To find the rate of change in lumber produced with respect to radius, we need to take the derivative of the given function with respect to radius. So, we need to find d/d(rp) 11eb69ff_fe7d_b46f_af94_5582b291bc61_TB8190_11 where rp denotes the radius in inches. 
Using the power rule of differentiation, we get:
d/d(rp) 11eb69ff_fe7d_b46f_af94_5582b291bc61_TB8190_11 = 2 * pi * rp * (50 + (rp/2)) 
Plugging in rp = 21, we get:
d/d(21) 11eb69ff_fe7d_b46f_af94_5582b291bc61_TB8190_11 = 2 * pi * 21 * (50 + (21/2)) = 3393.58 
So, the rate of change in the lumber produced per inch of increase in radius when the radius is 21 inches is approximately 3393.58 board-feet per inch. 
The answer is option B, 11eb69ff_fe7d_db81_af94_8f66621cd74c_TB8190_11.

Let Be the Amount of Lumber, in Board-Feet, Produced