Question

You are offered two different rules for estimating the number of board feet in a $ 16 $-foot log. (Aboard foot is a unit of measure for lumber equal to aboard $ 1 $ foot square and $ 1 $ inch thick.) The first rule is the Doyle Log Rule and is modeled by $ V_1 = \left(D - 4\right)^2 $, $ 5 \le D \le 40 $, and the other is the Scribner Log Rule and is modeled by $ V_2 = 0.79D^2 - 2D - 4 $, $ 5 \le D \le 40 $, where $ D $ is the diameter (in inches) of the $ \log $ and $ V $ is its volume (in board feet). (a) Use a graphing utility to graph the two log rules in the same viewing window. (b) For what diameter do the two scales agree? (c) You are selling large logs by the board foot. Which scale would you use? Explain your reasoning.

Name: Problem 74, Chapter 7: Precalculus with Limits
Uploaded: 2019-07-29T16:52:00-08:00
Duration: 1 min 9 s
Channel: Alisa Lu

   You  are  offered  two  different  rules  for estimating  the  number  of  board  feet  in  a  $ 16 $-foot  log.  (Aboard  foot  is  a  unit  of  measure  for  lumber  equal  to  aboard $ 1 $ foot  square  and $ 1 $ inch  thick.)  The  first  rule  is the Doyle  Log  Rule and  is  modeled  by $ V_1 = \left(D - 4\right)^2 $, $ 5 \le D \le 40 $,  and  the  other  is  the  Scribner  Log  Rule and is  modeled  by $ V_2 = 0.79D^2 - 2D - 4 $, $ 5 \le D \le 40 $, where $ D $ is  the  diameter  (in  inches)  of  the $ \log $ and $ V $ is its  volume  (in  board  feet).

(a)  Use  a  graphing  utility  to  graph  the  two  log  rules  in the  same  viewing  window.

(b)  For  what  diameter  do  the  two  scales  agree?

(c)  You  are  selling  large  logs  by  the  board  foot.  Which scale  would  you  use?  Explain  your  reasoning.

Precalculus with Limits

Ron Larson 2nd Edition

Chapter 7, Problem 74

Instant Answer

Solved by Expert Alisa Lu

07/29/2019

Step 1

The Doyle Log Rule is represented by the equation $V_1 = (D - 4)^2$ and the Scribner Log Rule is represented by the equation $V_2 = 0.79D^2 - 2D - 4$. We can use a graphing utility to plot these two equations on the same graph. Show more…

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You are offered two different rules for estimating the number of board feet in a $ 16 $-foot log. (Aboard foot is a unit of measure for lumber equal to aboard $ 1 $ foot square and $ 1 $ inch thick.) The first rule is the Doyle Log Rule and is modeled by $ V_1 = \left(D - 4\right)^2 $, $ 5 \le D \le 40 $, and the other is the Scribner Log Rule and is modeled by $ V_2 = 0.79D^2 - 2D - 4 $, $ 5 \le D \le 40 $, where $ D $ is the diameter (in inches) of the $ \log $ and $ V $ is its volume (in board feet). (a) Use a graphing utility to graph the two log rules in the same viewing window. (b) For what diameter do the two scales agree? (c) You are selling large logs by the board foot. Which scale would you use? Explain your reasoning.